Abstract: Beam envelope instability driven by space charge is an important factor causing the beam loss of intense beam superconducting linear accelerator. Zero-current period phase advance less than 90 degrees is the design principle of strong current superconducting linear accelerator generally followed in the world, and this design principle is proposed without considering acceleration. In this paper, the periodic instability under the condition of acceleration effect is analyzed by dynamic simulation. The results show that reasonable choice of focus change rate and acceleration gradient can reduce the influence of envelope instability, so that the strict limit of physical design period phase advance of less than 90 degrees can be broken and the acceleration efficiency of the accelerator can be improved.