We calculate the quark number density and quark number susceptibility (QNS) of QCD at finite chemical potential μ and finite temperature T in the framework of a new nonperturbative QCD model.Analysis and discussions of the calculated results of the QNS are given.It is found that the quark number density has a singularity when μ comes close to a critical value μo,and the QNS X(μ,T) becomes discontinuous at some values of T.At high temperature the QNS approaches the free quark gas result,while at very low temperature the QNS equals zero.Importantly,the QNS shows a sudden increase near some temperature (T ～ 120 MeV),which may be regarded as the signal of a crossover.