  We study the regularity of weak solutions to a certain class of second order
parabolic system under the only assumption of continuous coefficients. By using
the $A-$caloric approximation argument, we claim that the weak solution $u$ to
such system is locally H\"{o}lder continuous with any exponent $\alpha\in(0,1)$
outside a singular set with zero parabolic measure. In particular, we prove
that the regularity point in $Q_T$ is an open set with full measure, and we
obtain a general criterion for a weak solution to be regular in the
neighborhood of a given point. Finally, we deduce the fractional time and
fractional space differentiability of $D u$, and at this stage, we obtain the
Hausdorff dimension of singular set of $u$.
