A meshless method for transient electromagnetic fields is proposed herein. In this method, wave equations and the Lorentz gauge are discretized using the radial point interpolation method (RPIM) for space and Newmark's β method for time. The proposed method was applied to two typical problems. First, the proposed method was applied to the magnetic field of a square coil, yielding results which agree well with the reference solution. Second, the proposed method was applied to a Hertz dipole and propagation of the electromagnetic field was confirmed. Though the amplitude of the y-component of the magnetic flux density using the proposed method agrees well with that of the exact solution, the amplitude of the z-component of the electric field does not. This is because the amplitude of it is inversely proportional to the distance cubed. However, the potential of the proposed method is confirmed through the numerical examples.