Abstract: With the help of the conformal mapping，we transform the domain of solution into the upper half plane or band domain，thus the dimensions of electric potential is reduced to 1 from 2，then the first boundary value problem of Laplace equation is solved easily. Meanwhile，the distributions of electric potential and electric field intensity are obtained，and the maps of both electric field land equipotential lines are plotted by using mathematical software MATLAB.

Key words: conformal mapping, Laplace equation, first boundary value problem, distribution of electric potential, distribution of electric field intensity, visualization