Abstract: Based on the same theoretical model as proposed in some previous theoretical works but by more detailed theoretical calculations, we study charge transport through semiconductor nanowire with the interplay of Rashba spin-orbit coupling and induced superconducting pair potential. We show that two different types of zero-bias conductance peaks may exist for the theoretical model proposed in these theoretical works. One type of ZBCPs may occur when the Zeeman splitting exceeds the critical value and the semiconductor nanowire is in a topologically nontrivial superconducting phase, as was predicted in these some theoretical works. Another type of ZBCPs may also occur when the Zeeman splitting is smaller than the critical value and the semiconductor is in a topologically trivial superconducting phase. The two types of ZBCPs have some different characteristics and should be due to different mechanisms. The results obtained in the present paper may be useful for clarifying some controversial issues concerning the theoretical interpretation of some recent experimental results.