  In this paper, we propose a novel mass and energy conservative relaxation
Crank-Nicolson finite element method for the Schr\"{o}dinger-Poisson equation.
Utilizing only a single auxiliary variable, we simultaneously reformulate the
distinct nonlinear terms present in both the Schr\"{o}dinger equation and the
Poisson equation into their equivalent expressions, constructing an equivalent
system to the original Schr\"{o}dinger-Poisson equation. Our proposed scheme,
derived from this new system, operates linearly and bypasses the need to solve
the nonlinear coupled equation, thus eliminating the requirement for iterative
techniques. We in turn rigorously derive error estimates for the proposed
scheme, demonstrating second-order accuracy in time and $(k+1)$th order
accuracy in space when employing polynomials of degree up to $k$. Numerical
experiments validate the accuracy and effectiveness of our method and emphasize
its conservation properties over long-time simulations.
