Rayleigh-Taylor instability (RTI) is a fundamental physical process in fluids and plasmas. RTI is ubiquitous and must be considered in the field of high-energy-density physics, such as in space physics, astrophysics, and inertial confinement fusion. In this work, two-dimensional numerical simulations of laser-driven RTI with different density perturbations are performed using a radiation magnetohydrodynamic simulation program (FLASH). The effect of the applied magnetic field on the evolution of RTI at different Atwood numbers is systematically discussed. The results show that RTI evolves freely without an external magnetic field, and it is accompanied by the generation of secondary Kelvin–Helmholtz instability. Reducing the Atwood number weakens the mixing of fluids and has a strong stabilizing effect on the RTI. Introducing an external magnetic field parallel to the perturbation wave vector further inhibits the development of RTI and Kelvin–Helmholtz instability, with magnetic pressure playing a dominant role. The study results are important to gaining an in-depth understanding of the mixing of magnetic fluids and the magnetic field evolution at the instability interface and provide a reference for subsequent experimental studies on the related magnetization RTI.