This paper proposes a new model for image denoising and decomposition by non-convex functional minimization. Instead of using the Banach norm as the fidelity term, we use the square of L2 norm of the residual component divided by BV semi-norm as the fidelity term. This non-convex fidelity term has very low value for the texture image and high value for the geometric image, so it is appropriate for image denoising and decomposition. The gradient descent procedure is used to solve the proposed minimization problem, which leads to evolve a new nonlinear integral-differential equation to steady state. The experimental results demonstrate the proposed model not only obtains higher SNR but also makes visual improvements compared with the classical TV and OSV models.