In this paper, we present a finite volume trigonometric weighted essentially non-oscillatory (TWENO) scheme to solve nonlinear degenerate parabolic equations that may exhibit non-smooth solutions. The present method is developed using the trigonometric scheme, which is based on zero, first, and second moments, and the direct discontinuous Galerkin (DDG) flux is used to discretize the diffusion term. Moreover, the DDG method directly applies the weak form of the parabolic equation to each computational cell, which can better capture the characteristics of the solution, especially the discontinuous solution. Meanwhile, the third-order TVD-Runge-Kutta method is applied for temporal discretization. Finally, the effectiveness and stability of the method constructed in this paper are evaluated through numerical tests.