In this paper a new predictor-corrector noninterior method for LCP is presented, in which the predictor step is generated by the Levenberg-Marquadt method, which is new in the predictor-corrector-type methods, and the corrector step is generated as in [3]. The method has the following merits: (i) any cluster point of the iteration sequence is a solution of the P-0 LCP; (ii) if the generalized Jacobian is nonsingular at a solution point, then the whole sequence converges to the (unique) solution of the P-0 LCP superlinearly; (iii) for the P-0, LCP, if an accumulation point of the iteration sequence satisfies the strict complementary condition, then the whole sequence converges to this accumulation point superlinearly. Preliminary numerical experiments are reported to show the efficiency of the algorithm.