  In this paper we calculate the loss of fidelity due to quantum leakage for
the Josephson charge qubit (JCQ) in virtue of the Mathieu functions. It is
shown that for an present typical parameters of JCQ E_{J}/E_{ch}~0.02, the loss
of the fidelity per elementary operation is about 10^(-4) which satisfy the
DiVincenzo's low decoherence criterion. By appropriately improving the design
of the Josephson junction, namely, decreasing E_{J}/E_{ch} to 0.01, the loss of
fidelity per elementary operation can decrease to 10^(-6) even smaller.
