Abstract: The contact-impact analysis in multibody systems based on the nonsmooth dynamics approach is a hot topic in the research of multibody system dynamics. Newton-Euler approach is adopted to develop dynamics model of contactimpact analysis in non-smooth multi-body systems, and a new LCP formula is presented in this work. Different from Lagrange methods, Newton-Euler modeling method incorporate equality constraints into dynamic models with noninterpenetration constraints and frictional constraints together. In Newton-Euler modeling method, the basic system is derived by removing the non-interpenetration constraints and frictional constraints from the original multi-body system. Newton-Euler eqution of basic system is established by using the maximum coordinates method. Because the coordinates of the basic system are not independent of each other, equality constraints are involved in modeling, the basic system dynamic equations is a set of DAE (differential algebra equation). With the aid of constraint Jacobian matrix, Lagrangian multipliers corresponding to the non-interpenetration constraint forces and Coulomb friction forces are added to the basic system DAE to obtain the dynamic equations of global motion of the multi-body system with characteristics of variable topological structure. The complete dynamic model is composed of basic system DAE, equality and inequality constraints. In order to simplify the derivation process of LCP, a decomposed matrix form is built. The LCP -based Time-stepping method is adopted for numerical simulation. Time-stepping algorithm is a popular non-smooth numerical algorithm, Its prominent feature is that it can avoid the tedious event-detection process in numerical integration. In the process of numerical integration, the contact-detachment state of the system can be determined by solving the LCP. Our method is carried out in slider-crank mechanism with a translational clearance joint, the simulation results indicate that this method is effective.