A second-order optimized monotonicity-preserving MUSCL scheme (OMUSCL2) is developed based on the dispersion and dissipation optimization and monotonicity-preserving technique. The new scheme (OMUSCL2) is simple in expression and is easy for use in CFD codes. Compared with the original second-order or third-order MUSCL scheme, the new scheme shows nearly the same CPU cost and higher resolution to shockwaves and small-scale waves. This new scheme has been tested through a set of one-dimensional and two-dimensional tests, including the Shu-Osher problem, the Sod problem, the Lax problem, the two-dimensional double Mach reflection and the RAE2822 transonic airfoil test. All numerical tests show that, compared with the original MUSCL schemes, the new scheme causes fewer dispersion and dissipation errors and produces higher resolution.