To improve dissipation characteristic and resolution for flow features of classical third-order WENO scheme (WENO-JS3). An improved third-order WENO-Z+ scheme (NWENO-Z+3) was constructed with a different global smoothness indicator. Several classical one-dimensional Riemann problems and double Mach reflection case were simulated to investigate computing performance of NWENO-Z+3 scheme. It indicated that NWENO-Z+3 scheme have better characteristics than schemes such as WENO-JS3, WENO-Z and WENO-Z+3 scheme with low numerical dissipation and high resolution to flow features. NWENO-Z+3 scheme was also used to investigate propagation and wave evolution of blast waves generated by cylindrical high pressure gas in single cabin and connected cabins. It indicated that NWENO-Z+3 scheme was suitable for simulating evolution of blast waves, which contains high pressure ratio and high density ratio.