Rayleigh-Taylor instability (RTI) is a fundamental physical phenomenon in fluids and plasmas, and plays a significant role in astrophysics, space physics, and engineering. Especially in inertial confinement fusion (ICF) research, numerous experimental and simulation results have identified RTI as one of the most significant barriers to achieving fusion. Understanding the origin and development of RTI will be conducive to formulating mitigation measures to curb the growth of instability, thereby improving the odds of ICF success. Although there have existed many theoretical and experimental studies of RTI under high energy density, there are few experiments to systematically explore the influence of magnetic fields on the evolution of magnetized RTI. Here, a new experimental scheme is proposed based on the Shenguang-II laser facility on which the nanosecond laser beams are used to drive modulation targets of polystyrene (CH) and low-density foam layers. A shock wave is generated after the laser’s CH modulation layer has been ablated, and propagates through CH to low-density foam. Moreover, Richtmyer-Meshkov instability is triggered off when the shock wave accelerates the target. When the laser pulse ends, the shock wave evolves into a blast wave, causing the system to decelerate, resulting in RTI in the reference system of the interface. In this paper the open-source radiation MHD simulation code (FLASH) is used to simulate the RTI generated by a laser-driven modulation target. The evolution of RTI under no magnetic field, under Biermann self-generated magnetic field, and under different applied magnetic fields are systematically investigated and compared with each other. The simulation results show that the Biermann self-generated magnetic field and the applied magnetic field parallel to flow direction do not change the interface dynamics in the evolution process of RTI. Nevertheless, the applied magnetic field perpendicular to flow direction can stabilize RTI and the Kelvin-Helmholtz vortex at the tail of the RTI spike. Magnetic pressure plays a decisive role. The present results provide a reference for the follow-up study of target physics related to ICF and deepen the understanding of the fluid mixing process.