This paper investigates the problem of state estimation of nonlinear systems with nonlinear equality constraints. By treating the nonlinear equality constraints as part of the new coordinate, a diffeomorphism is found such that an unconstrained reduced-order system is obtained. The existing unconstrained estimators can be applied to obtain the reduced-order state estimate. Then, based on the inverse transformation, the original states can be obtained by combing the reduced-order state estimate and the nonlinear equality constraints. Compared with the traditional model reduction approach, there exists one more freedom to choose the independent variables in the proposed approach. Compared with the null space approach, the proposed approach can handle nonlinear estimation with general nonlinear equality constraints. Finally, the estimation problem for a moving vehicle on a given circular path is used to illustrate the principle of the proposed approach.