The linear complementarity problem L C P ( M , q ) is to find a vector z in IR n satisfying z T ( M z + q ) = 0 , M z + q ⩾ 0 , z ⩾ 0 , where M = ( m i j ) ∈ IR n × n and q ∈ IR n are given. In this paper, we use the fact that solving L C P ( M , q ) is equivalent to solving the nonlinear equation F ( x ) = 0 where F is a function from IR n into itself defined by F ( x ) = ( M + I ) x + ( M − I ) | x | + q . We build a sequence of smooth functions F ̃ ( p , x ) which is uniformly convergent to the function F ( x ) . We show that, an approximation of the solution of the L C P ( M , q ) (when it exists) is obtained by solving F ̃ ( p , x ) = 0 for a parameter p large enough. Then we give a globally convergent hybrid algorithm which is based on vector divisions and the secant method for solving L C P ( M , q ) . We close our paper with some numerical simulations to illustrate our theoretical results, and to show that this method can solve efficiently large-scale linear complementarity problems.