A low-energy relativistic free electron capture and violently acceleration by a tightly focused ultra-short ultra-intense laser pulse in vacuum is presented in this paper. The results show that the electron is mainly accelerated by the long itudinal ponderomotive force and the energy gain is sensitively dependent on the retarded time, initial energy and the incident angle of electron. On the other hand, the energy gain is not very sensitive to the pulse width when it is larger than 10λ.