In this paper, we first give a lower bound of the lifespan and some estimates of classical solutions to the Cauchy problem for general quasi-linear hyperbolic systems, whose characteristic fields are not weakly linearly degenerate and the inhomogeneous terms satisfy Kong’smatching condition. After that, we investigate the lifespan of the classical solution to the Cauchy problem and give a sharp limit formula. In this paper, we only require that the initial data are sufficiently small in the L1 sense and the BV sense.