The G⁰ distribution is capable of fitting radar clutter with different degrees of heterogeneity, so the accurate simulation of bi-dimensional correlated G⁰ distributed radar clutter is a vital step in the radar system design and evaluation. In the base of the nonlinear transformation which was expressed approximately by the method of piecewise polynomial fitting, the simulation method of bi-dimensional correlated G⁰ distributed radar clutter based on memoryless nonlinear transformation was proposed by taking the bi-dimensional correlated Gaussian process as input. Furthermore, in order to control the amplitude and correlation of radar clutter independently and simulate coherent radar clutter with in-phase and quadrature component, the characteristic function of the haplopia G⁰ distribution was derived and the simulation methods based on spherically invariant random process were proposed. Simulation results show that both two methods can generate bi-dimensional correlated G⁰ distribution radar clutter which meets the requirements of amplitude and correlation.