In this paper we study solvability of the Cauchy problem of the Kawahara equation 偏导dtu ＋ au偏导dzu ＋ β偏导d^3xu ＋γ偏导d^5xu = 0 with L^2 initial data. By working on the Bourgain space X^r,s（R^2） associated with this equation, we prove that the Cauchy problem of the Kawahara equation is locally solvable if initial data belong to H^r（R） and -1 〈 r ≤ 0. This result combined with the energy conservation law of the Kawahara equation yields that global solutions exist if initial data belong to L^2（R）.
