New accurate and compact formulas are established for general two-state curve crossing problems in the Landau-Zener case, in which the two diabatic potentials cross with the same sign of slopes. These formulas can cover practically the whole range of energy and coupling strength, and can be directly applied to various problems involving the curve crossing. All the basic potential parameters can be estimated directly from the adiabatic potentials and nonunique diabatization procedure is not required. Complex contour integrals are not necessary to evaluate the nonadiabatic transition parameter; thus the whole theory is very convenient for various applications. The compact formula for the Landau-Zener transition probability, which is far better than the famous Landau-Zener formula, is proposed. Now, together with the previous paper [Zhu and Nakamura, J. Chem. Phys. 101, 10 630 (1994)], the present semiclassical theory can present a complete set of solutions of the the two-state curve crossing problems.