  It is well known that investigating QCD at finite density by standard Monte
Carlo methods is extremely difficult due to the sign problem. Some years ago,
the complex Langevin method with gauge cooling was shown to work at high
temperature, i.e., in the deconfined phase. The same method was also applied to
QCD in the so-called heavy dense limit in the whole temperature region. In this
paper we attempt to apply this method to the large $\mu/T$ regime with moderate
quark mass using four-flavor staggered fermions on a $4^3\times 8$ lattice.
While a straightforward application faces with the singular-drift problem,
which spoils the validity of the method, we overcome this problem by the
deformation technique proposed earlier. Explicit results for the quark number
density and the chiral condensate obtained in this way for $3.2\leq \mu/T\leq
5.6$ are compared with the results for the phase-quenched model obtained by the
standard rational hybrid Monte Carlo calculation. This reveals a clear
difference, which is qualitatively consistent with the Silver Blaze phenomenon.
