Curved panels can bear more lateral load than flat plates because they can transmit the external load along curved surface in addition to load-carrying capacity by the bending stiffness. For curved panels, however, there is a critical point of the lateral load that structure can endure before it buckles. On the other hand, composites are known to have more advantages in specific strength and stiffness than conventional metal materials. The present paper proposes a semi-analytical method to predict the initial buckling loads of slightly curved panels composed of thin orthotropic composite layers under general boundary conditions. Based on the Donnell type theory, the potential strain energy is evaluated as a sum of stretching energy, stretching-bending coupling energy and bending energy, and the external work done by uniform external pressure is included in the functional. The eigenvalue equation is derived by the Ritz method to yield such initial buckling load parameters as eigenvalues. Numerical examples include a list of buckling loads and the corresponding buckling patterns for typical panels with simply supported and clamped edges.