We study QCD at finite density and low temperature by using the complex Langevin method. We employ the gauge cooling to control the unitarity norm and introduce a deformation parameter in the Dirac operator to avoid the singular drift problem. The reliability of the obtained results are judged by the probability distribution of the magnitude of the drift term. By extrapolating the reliable results with respect to the deformation parameter, we obtain the results for the original system. We perform the simulation on a $4^3\times8$ lattice and show that our method works well even in the region where the reweighing method fails due to the severe sign problem. As a result, we observe a clear onset of the baryon number density at the chemical potential near one-third of the nucleon mass.