In the study of classical rumor spreading models, rumor spreading rate and removal rate are generally regarded as constants.Based on practical situations, a rumor spreading function and a removal rate function were proposed and a rumor spreading model with variable spreading rate and removal rate was studied in homogeneous and scale-free networks respectively.Mean-field equations were derived and numerical simulations were conducted in Matlab.The results show that in the rumor spreading model with variable spreading rate and removal rate, spreading threshold still exists and the final size of rumor spreading is larger than that in the rumor spreading model with constant spreading rate and removal rate.Furthermore, the comparison between rumor spreading processes in homogeneous network and heterogeneous network shows that network topological structure has a great impact on rumor spreading.The final size of rumor spreading in homogeneous network is larger than that in scale-free network.