This work is an example for application of nonlinear programming for the problem of three- dimensional trajectory optimization of multi-stage launch vehicles for geostationary orbit missions. The main objective is to minimize fuel consumption or equivalently to maximize the payload. The launch vehicle studied here, Europa- II, consists of 5 thrust phases and 2 coast phases. The major parameters of the coast arcs such as inclination, eccentricity and true anomaly of attachment points are not prespecified and should be found in the optimization problem. The fairing should be jettisoned whenever aerothermal flux falls below a certain value. A maximum aerodynamic heating constraint for the atmospheric part of the flight is also considered. The problem is solved with the direct collocation method and results are compared with those in Ref. 1 (W.Duffek, G.C.Shau), where an indirect multiple shooting method with an inner loop for parameter optimization is used. Advantages of present work with respect to methods used in specified references are then discussed.