In this paper, a 3D laser plasma interaction system is presented, analysed, and implemented. The system has two unstable equilibria, and two types of coexisting attractors in which the coexistence of two periodic orbits and the coexistence of two chaotic attractors can be clearly observed. The multistability behaviours are determined by the bifurcation diagrams, largest Lyapunov exponents, and phase spaces. Moreover, the complexity performance of the laser plasma interaction system is investigated by the contour plot of the Sample Entropy.