A new short-lived neutron-deficient isotope ^{220}Np was synthesized in the fusion-evaporation reaction ^{185}Re(^{40}Ar,5n)^{220}Np at the gas-filled recoil separator SHANS. Based on the measurement of the correlated α-decay chains, the decay properties of ^{220}Np with E_{α}=10040(18) keV and T_{1/2}=25_{-7}^{+14} μs were determined, which are in good agreement with theoretical predictions. From the new experimental results coupled with the recently reported α-decay data of ^{219,223}Np, the α-decay systematics for Np isotopes around N=126 was established, which allows us for the first time to test the robustness of the N=126 shell closure in Z=93 Np isotopes. The results also indicate that, in the region of nuclei with Z≥83, the proton drip line has been reached for all odd-Z isotopes up to Np.