This paper presents a Newmark-based predictor-corrector (NPC) method for the solution of constrained structures characterized by differential and algebraic equations (DAE's). The feature of this method is the formulation and solution of the generalized displacements of the structure incorporating Lagrangian multipliers in the mixed DAE's separately using a predictor-corrector-like procedure. By giving predictions of the generalized displacements, the Lagrangian multipliers are evaluated from their governing equation, and then the generalized displacements are corrected based on the evaluated Lagrangian multipliers. A rigorous proof of the unconditional stability of the integration scheme for linear DAE's is derived. To demonstrate the effectiveness of the proposed method, a 14-bar truss structure with circular slot constraints is solved.