In In0.6Ga0.4As/GaAs quantum dot, using a one-dimensional effective potential model and the finite difference method, we theoretically study the properties of an exciton under the influence of an applied magnetic field, such as the transition energy, the binding energy, the spatial distributions of the electron and the hole. The effects due to the applied magnetic filed and the quantum confinement on the binding energy are analyzed, and the following results are obtained: the ground state transition energy of the heavy-hole exciton can split into four energy levels due to the Zeeman effect, of which the results are in good agreement with experimental results; the binding energy increases monotonically with the increase of lateral confinement or magnetic field; the size of the quantum dot has a significant influence on the binding energy of the exciton, which can be seen both from the average distance between the electron and the hole and from the wave function distributions of the exciton.