Abstract: P-matrices play a critical role in scientific engineering calculations. Based on Ostrowski-Brauer Sparse (OBS) matrices, a new subclass of P-matrices called Ostrowski-Brauer Sparse B (OBS-B) matrices is introduced, which contains B-matrices and DB-matrices. Moreover, using the infinity norm bound of the inverse of OBS matrices, a computable error bound for the linear complementarity problem of OBS-B matrices is given. And it is shown that the given bound improves the classical bound provided for B-matrices by García-Esnaola and Peña in some cases. Finally, numerical examples are reported to illustrate the effectiveness of the obtained bound.