With the development of large low earth orbit (LEO) communication constellations, the efficiency of laser inter-satellite link (ISL) establishing become the bottleneck for subsequent large-scale launch and rapid networking applications of LEO communication constellations. Hence, we establish the pointing jitter error structure of LEO communication experiment satellites (LCES) system. The error structure can be used to trace the source of errors and evaluate the in-orbit jitter. And we derive an analytical expression of the acquisition probability density function (PDF) which comprehensively considering the influence of the scanning region, the pointing jitter error, the overlap factor and the in-orbit jitter error. The multi-parameter influenced acquisition model is validated by Monte Carlo (MC) simulations and semi-physical tests. The results reveals that the multi-parameter influenced acquisition model can be used to guide the in-orbit ISL establishing.