Numerical calculation for two integral transforms in 2.5-D transient electromagnetic forward is a difficult and key task, namely, the inverse Fourier transform and the inverse Laplace transform. Some effective algorithms for them were described. Based on the known algorithms in DC resistivity on wave-number distribution and selection, we proposed a principle on how to choose the least wave-number concerning the central-loop transient electromagnetic method. First, observe the behavior of transformation function curve with regard to wave-number in Fourier domain. In the light of its asymptote, ascertain the coverage scope of wave-number. Compared with analytic solution, the least wave-number in Fourier domain can be derived. Furthermore, the Laplace numerical inversion algorithm which needs only a few Laplace variables in pure real domain was also introduced here. The procedure was applied to forward modeling on transient electromagnetic field of a vertical magnetic dipole over uniform half-space to demonstrate them effectiveness and general applicability.