The chemical potential (μ) 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 $0\leq a μ \lesssim 1.0$, while at $T \approx T_c$, it decreases significantly from the μ=0 value in a high μ regime. In this work, we perform the simulation for $μ/T\leq16$, which covers even the low temperature and the high chemical potential regime. In this regime, we in troduce 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 ($T\approx T_c/2$), which is obtained after taking the j→0 limit of the diquark condensate and the Polyakov loop.