  We introduce a new weak Galerkin finite element method whose weak functions
on interior neighboring edges are double-valued for parabolic problems. Based
on $(P_k(T), P_{k}(e), RT_k(T))$ element, a fully discrete approach is
formulated with implicit $\theta$-schemes in time for
$\frac{1}{2}\leq\theta\leq 1$, which include first-order backward Euler and
second-order Crank-Nicolson schemes. Moreover, the optimal convergence rates in
the $L^2$ and energy norms are derived. Numerical example is given to verify
the theory.
