Inter-carrier interference (ICI) and multiuser interference (MUI) occur in an uplink orthogonal frequency division multiple access (OFDMA) system if a channel between a user and a base station is rapidly time-varying. Based on the successive interference cancelation (SIC), we propose a new subcarrier allocation algorithm using the convex programming, which minimizes the ICI and MUI smeared in the subcarriers allocated to the fast moving users. Simulation results show that the proposed subcarrier allocation provides the better bit error rate (BER) performance than other allocations in convolutional coded system using a SIC-aided detector.