The quasi-Green’s function method is employed to solve the free vibration of slip clamped shallow spherical shell with arbitrary boundary shape. A Green quasi-function is established by using the fundamental solution and boundary equation of the problem. This function satisfies the homogeneous boundary condition of the problem. The mode shape differential equation of the free vibration problem of slip clamped shallow spherical shell with arbitrary boundary shape is reduced to Fredholm integral equation of the second kind by Green’s formula. Irregularity of the kernel of integral equation is overcome by choosing a suitable form of the normalized boundary equation. Finally, the numerical results can be obtained by the discretization equations. Numerical examples demonstrate that the method has high precision, small amount of calculation, and fast convergence rate, and it is a new kind of effective mathematical methods.