In order to repeat the propagation and its distribution characteristics, the lightning electromagnetic field (LEMP) in the entire space is calculated by a modified finite difference time-domain (FDTD) approach in this paper. Different from issued results, in which the electromagnetic field operates only at some discrete points near the ground, the LEMP and its time derivatives, power density and energy density at each unit in the whole space under the ground are calculated and expressed as groups of pictures. We find LEMPs attenuate exponentially in the horizontal and vertical direction, in the area near the ground and far from the discharge channel. The peak values of horizontal electric field and azimuthal magnetic field each have an unaltered polarity and their contours are similar to double exponential functions in the entire space under the ground. However the peak values of vertical electric field can be divided into two opposite-polarity parts in the whole area under the ground, and the contours in the area near the strike channel are spherical in shape. The other components have similar features. We also calculate the LEMPs with different values of ground conductivity, ground permittivity, return model and base current, and the characteristics of distribution are not changed, although the values are enhanced integrally in some cases. And in the layered earth, the LEMP has similar contours inside the layers. Even in the case of striking to the lightning rod, the characteristics of distribution are not changed. These patterns and distribution characteristics of LEMP can provide support and reference in shielding design and route planning under the ground.