The kinetics of the radical-polar molecule reaction $CH_3+HBr{ ightarrow}CH_4+Br$ has been studied at temperatures between 150 and 1000 K using classical dynamics procedures. Potential energy surfaces constructed using analytical forms of inter- and intramolecular interaction energies show a shallow well and barrier in the entrance channel, which affect the collision dynamics at low temperatures. Different collision models are used to distinguish the reaction occurring at low- and high-temperature regions. The reaction proceeds rapidly via a complex-mode mechanism below room temperature showing strong negative temperature dependence, where the effects of molecular attraction, H-atom tunneling and recrossing of collision complexes are found to be important. The temperature dependence of the rate constant between 400 and 1000 K is positive, the values increasing in accordance with the increase of the mean speed of collision. The rate constant varies from $7.6{ imes}10^{-12}$ at 150 K to $3.7{ imes}10^{-12}$ at 1000 K via a minimum value of $2.5{ imes}10^{-12};cm^3;molecule^{-1};s^{-1}$ at 400 K.