  In this paper, we prove the non-uniqueness of three-dimensional
magneto-hydrodynamic (MHD) system in $C([0,T];L^2(\mathbb{T}^3))$ for any
initial data in $H^{\bar{\beta}}(\mathbb{T}^3)$~($\bar{\beta}>0$), by
exhibiting that the total energy and the cross helicity can be controlled in a
given positive time interval. Our results extend the non-uniqueness results of
the ideal MHD system to the viscous and resistive MHD system. Different from
the ideal MHD system, the dissipative effect in the viscous and resistive MHD
system prevents the nonlinear term from balancing the stress error
$(\RR_q,\MM_q)$ as doing in \cite{2Beekie}. We introduce the box flows and
construct the perturbation consisting in six different kinds of flows in convex
integral scheme, which ensures that the iteration works and yields the
non-uniqueness.
