The chemical potential ($mu$) dependence of the topological susceptibility with two-color two-flavor QCD is studied. We find that at temperature $T approx T_c /2$, where $T_c$ denotes the critical temperature at zero chemical potential, the topological susceptibility is almost constant throughout $0 leq amu lesssim 1.0$, while at $Tapprox T_c$, it decreases significantly from the $mu=0$ value in a high $mu$ regime. In this work, we perform the simulation for $mu/T le 16$, which covers even the low temperature and the high chemical potential regime. In this regime, we introduce a diquark source term, which is characterized by $j$, into the action. We also show our results for the phase diagram in a low temperature regime ($Tapprox T_c/2$), which is obtained after taking the $j to 0$ limit of the diquark condensate and the Polyakov loop.
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