The rapid neutron-capture process (r-process), which is an interdisciplinary field of astrophysics and nuclear physics, is bound up with various characteristics of thousands of neutron-rich exotic nuclei, such as nuclear masses, and the relevant reactions. By employing the WLW microscopic-macroscopic nuclear mass model developed recently, the solar r-process abundance distribution is well reproduced in the classical r-process approach. In comparison with the well known FRDM model, the present calculation better pictures the nuclear region of A135 and A180, and especially avoids the abundance peaks at A135 often obtained in other calculations. The improvement in the r-process calculation may indicate a more suitable description of the evolution of shell structure and symmetry energy towards the drip line in the WLW model.