Supersonic gas jets generated via a conical nozzle are widely applied in the laser wakefield acceleration of electrons. The stability of the gas jet is critical to the electron injection and the reproducibility of the wakefield acceleration. Here we discussed the role of the stilling chamber in a modified converging–diverging nozzle to dissipate the turbulence and to stabilize the gas jets. By the fluid dynamics simulations and the Mach–Zehnder interferometer measurements, the instability originating from the nonlinear turbulence is studied and the mechanism to suppress the instability is proposed. Both the numerical and experimental results prove that the carefully designed nozzle with a stilling chamber is able to reduce the perturbation by more than 10% compared with a simple-conical nozzle.