To investigate the free in-plane vibration of circular sector plates, analytical solutions are derived based on Helmholtz decomposition and the method of separation of variables. Eigenvalue problems in the circumferential direction are derived by applying the boundary conditions on both radial edges. Meanwhile, it is proved that compatible eigenvalue conditions can be only obtained when both radial edges are simply supported. The analytical solutions of displacements and stresses are derived by invoking the method of separation of variables. Subsequently, the corresponding characteristic equations for finding natural frequencies and mode shapes are derived using the boundary conditions at outer radius. Extensive results of circular sector plates with different boundary conditions and various sector angles are presented to demonstrate the proposed method. The results indicate that the proposed method has great accuracy and applicability. Parameter study shows that the first fifth natural frequencies keep constant in some region and decrease monotonically in other region as the sector angle increasing.