To improve annular jet pump (AJP) performance, new ways named constant rate of velocity/pressure change method (CRVC/CRPC) were adopted to design its diffuser. The design formulas were derived according to the assumption of linear velocity/pressure variation in the diffuser. Based on the two-dimensional numerical simulations, the effect of the diffuser profile and the included angle on the pump performance and the internal flow details has been analyzed. The predicted results of the RNG k-epsilon turbulence model show a better agreement with the experiment data than that of the standard and the realizable k-epsilon turbulence models. The AJP with the CRPC diffuser produces a linear pressure increase in the CRPC diffuser as expected. The AJP with CRPC/CRVC diffuser has better performance when the diffuser included angle is greater or the diffuser length is shorter. Therefore, the AJP with CRPC/CRVC diffuser is suitable for applications requiring space limitation and weight restriction.