We use the direct method proposed by He et al. [Phys. Lett. B 680 (2009) 432) to calculate the quark-number susceptibility (QNS) at finite temperature and the chemical potential in the quasi-particle model. In our approach the QNS is given by a formula solely involving the dressed quark propagator at finite chemical potential μ and temperature Τ. The QNS at finite μ and Τ is calculated in the quasi-particle model. It is found that at high temperatures the QNS tends to the ideal quark gas result. At very small temperatures the QNS vanishes. This vanishing behavior in the low-temperature region is consistent with the lattice results. For μ∈ [0,180] MeV, our results show that there exists a rapid increase of QNS near some temperatures. The temperature at which the rapid increase occurs shifts to smaller values with the increasing quark chemical potential. This rapid increase could be regarded as a signal of a crossover.