The rheological properties of Earth’s lower mantle are key for mantle dynamics and planetary evolution. The main rock‐forming minerals in the lower mantle are bridgmanite (Br) and smaller amounts of ferropericlase (Fp). Previous work has suggested that the large differences in viscosity between these minerals greatly affect the bulk rock rheology. The resulting effective rheology becomes highly strain‐dependent as weaker Fp minerals become elongated and eventually interconnected. This implies that strain localization may occur in Earth’s lower mantle. So far, there have been no studies on global‐scale mantle convection in the presence of such strain‐weakening (SW) rheology. Here, we present 2D numerical models of thermo‐chemical convection in spherical annulus geometry including a new strain‐dependent rheology formulation for lower mantle materials, combining rheological weakening and healing terms. We find that SW rheology has several direct and indirect effects on mantle convection. The most notable direct effect is the changing dynamics of weakened plume channels as well as the formation of larger thermochemical piles at the base of the mantle. The weakened plume conduits act as lubrication channels in the mantle and exhibit a lower thermal anomaly. SW rheology also reduces the overall viscosity, notable in terms of increasing convective vigor and core‐mantle boundary heat flux. Finally, we put our results into context with existing hypotheses on the style of mantle convection and mixing. Most importantly, we suggest that the new kind of plume dynamics may explain the discrepancy between expected and observed thermal anomalies of deep‐seated mantle plumes on Earth. Earth’s lower mantle (660–2,890 km depth) controls our planet’s evolution by regulating the transport of materials and heat through mantle convection. To better understand mantle convection and the evolution of Earth over billions of years, mathematical laws describing how rocks flow (viscosity) are needed. Recently, it was discovered that the deformation history of lower‐mantle rocks affects the viscosity. In the lower mantle there are two main minerals: Bridgmanite (Br), which is relatively strong (high viscosity), and ferropericlase (Fp), which is relatively weak (low viscosity). When a rock containing both minerals is deformed, the weak Fp grains can form interconnected layers, lowering the overall viscosity and thus weakening the whole rock. Here, we present prompting new results that show how mantle convection and Earth’s evolution are affected by such a deformation‐dependent or “strain‐weakening” (SW) viscosity law, using global‐scale numerical simulations of mantle convection and plate tectonics. We find that, in particular, the dynamics of hot, rising columns of mantle material (plumes) are affected by SW rheology, making them more narrow, fast, and less hot relatively to other plumes. Finally, we find that this new types of plume dynamics could be linked to several observations of mantle plumes in the Earth. A new strain‐weakening (SW) rheology for lower mantle materials is implemented in numerical models of global‐scale mantle convection Such rheology causes weakening of plume conduits, forming narrow lubrication channels in the mantle through which hot material easily rises SW rheology in the lower mantle could explain the discrepancy between expected and observed thermal anomalies of deep mantle plumes on Earth A new strain‐weakening (SW) rheology for lower mantle materials is implemented in numerical models of global‐scale mantle convection Such rheology causes weakening of plume conduits, forming narrow lubrication channels in the mantle through which hot material easily rises SW rheology in the lower mantle could explain the discrepancy between expected and observed thermal anomalies of deep mantle plumes on Earth.