Inspiring by the k-plane clustering (kPC) on L2 norm metrics, a L1 norm clustering algorithm is proposed by introducing L1 metric into clustering, which is termed as L1 kPC (k-plane clustering using L1 norm). The plane-updating of L1 kPC can be characterized by a nonconvex optimization problem. An alternative strategy is provided to conquer such non-convexity. That is, the nonconvex problem can be transformed into a series of convex problems on a finite number of subsets. Meanwhile, in order to avoid solving multiple optimization problems on individual subsets thereby resulting in heavy training burden, a search strategy is also provided to seek suitable subset and this search task can be completed in a linear time. Thus the foresaid optimization problem only needs to solve k linear programming instead of solving the k eigenvalue problems in kPC. Experimental results on artificial and UCI datasets show that the proposed method has less training and testing time-consume, and comparable or even better clustering performance on the majority data sets.