This paper studies the stability and error estimates of the local discontinuous Galerkin method for fourth-order linear partial differential equations based on upwind-biased fluxes. Consider using the semi-discrete form of numerical format in the spatial direction and using the generalized Gauss-Ｒadau projection，the projection error caused by the numerical flux is eliminated. The optimal error estimate of the numerical format is obtained by using Young inequality. It is proved that when the convective term is selected as the upwind-biased numerical fluxes，the convergence order of the method is order k + 1. Because the spatial discrete operator of the partial differential equation LDG method with higher-order spatial derivatives is rigid，the second-order implicit Crank-Nicolson method is used for time dispersion，and the correctness of the theoretical analysis results is verified by numerical experiments.