New cluster expansion method is formulated in Euclidean lattice gauge theories where the expansion parameter is the space-time extent of clusters. This method is powerful if the correlation length of the applied system is finite. In this paper the new expansion method is applied to the calculation of the free energy and the string tension in D=3 SU(2) lattice gauge theory with standard action. The convergence of the expansion series is so fast even in the weak coupling region. The results can be compared quantitatively to Monte Carlo simulation. The relation between the new method and the conventional strong coupling expansion (S.C.E.) is also discussed.