Grounded Electrical-source Airborne Transient Electromagnetic（GREATEM）is a new geophysical exploration method. When using the traditional numerical simulation methods to deal with the forward modeling, there exits some problems such as mesh generation and low accuracy. In view of the above problems, the meshfree collocation method based on the radial basis function is applied to calculate the response of GREATEM. We derive the control iterative equations based on the Maxwell’s equations, the boundary condition and stability condition are also discussed. We compare the meshfree solution with the analytical and the finite difference method in a homogeneous half space model, and calculate a circular low resistivity abnormal body model. The calculation results show that the meshfree collocation method to discrete control equation is simple and has high calculation precision, it is easy to simulate the complex models. The meshfree method is expected to be widely used in the numerical simulation of grounded airborne transient electromagnetic exploration, it will provide a new idea for the geophysical exploration modeling.