  In this paper, we obtain global small solutions and decay estimates for the
MHD boundary layer in Gevrey space without any structural assumptions,
generalizing the results of \cite{NL} in analytic space. The proof method is
mainly inspired by \cite{WXLY} and \cite{CW}, using new auxiliary functions and
finer structural analysis to overcome the difficulty of the loss of derivatives
and then we obtain the global well-posedness of the MHD boundary layer in the
Gevrey $\frac{3}{2}$ space.
