The backward Cauchy problem of linear degenerate stochastic partial differential equations is discussed in this talk. We obtain the existence and uniqueness results in Sobolev space $L^p(\Omega;C([0,T];W^{m,p}))$ with both $m\geq1$ and $p\geq2$ being arbitrary, without imposing the symmetry condition for the coefficient $\sigma$ of the gradient of the second unknown---which was introduced by Ma and Yong [PTRF 113 (1999)] in the case of $p=2$. To illustrate the application, we give a maximum principle for optimal control of degenerate stochastic partial differential equations. (This is a joint work with Prof. Shanjian Tang and Dr. Kai Du)