Magnetic circular dichroism (MCD) spectra are able to provide insights into the geometric, electronic, and magnetic properties of chemical systems. However, they can be challenging to understand and simulate given the need to simultaneously treat both the finite magnetic and optical fields. Thus, efficient simulations are desired to understand the spectra and resolve the molecular electronic states. Real-time dynamics are used widely in the simulation of electronic spectroscopies such as absorption as well as electronic circular dichroism, but simulating MCD with real-time dynamics is technically and theoretically challenging. In this work, we introduce a real-time dynamics-based ab initio method with a nonperturbative treatment of a static magnetic field with London orbitals for simulating the MCD spectra of closed shell systems. Effects of a magnetic field are included variationally in the spin-free nonrelativistic Hamiltonian. Real-time time-dependent density functional theory dynamics are then performed, from which we compute the response function in the presence of the external magnetic field, giving the MCD spectrum. The method developed in this paper is applied to simulate the MCD spectra for pyrimidine, pyrazine, and 1,4-naphthoquinone. Results are discussed and compared to the experiment.