Abstract: β-decay half-lives of r-process waiting-point nuclei are the crucial physical data for understanding the origin of heavy elements in the universe. Proton-neutron quasi-particle random phase approximation (pn-QRPA) is an important theoretical model to study nuclear β decays. In this work, we propose an improved pn-QRPA model to systematically study β decays from nuclei near closed shells. Compared with previous works, new forms of particle-particle and particle-hole interactions are adopted in the improved model, which depend on both the neutron number and the proton number. We first validate our new model by calculating β-decay half-lives and Gamow-Teller strength distributions of some known nuclei around closed shells. The theoretical results agree well with experimental data. We then predict the β-decay half-lives of various unknown waiting points nuclei near N=50,~N=824, and N=126, such as ¹²⁴Mo, ¹²⁶Ru, ¹²⁸Pd, ¹⁸⁶Nd, ¹⁸⁸Sm, ¹⁹²Dy, ¹⁹⁴Er, ¹⁹⁶Yb, ¹⁹⁸Hf. The predictions are consistent with the previous model. These results are good references for the future physics research of r-process near the closed shell.