Engineering structures are often subjected to multi-dimensional random loads, and the accurate simulation of multi-dimensional random load time history is of great significance to the reliability design of structures. Based on the rigorous theoretical formula derivation of spectrum representation method about the multi-dimensional random load, the cause for the large deviation between the spectrum density matrix of the synthetic load and that of target load was analyzed in detail, providing a theory support for the multi-dimensional random load time domain simulation correction. A multi-dimensional random load time domain simulation algorithm based on the spectrum correction method was proposed. By calculating the deviation between the spectrum density matrix of the synthetic time domain load and that of the target load, the iterative technique was developed to modify the spectrum density matrix of the synthetic time domain load through feedback of errors. Furthermore, the spectrum density matrix of the synthetic time domain load was made to approach to that of the target load. Finally, a numerical analysis about three dimensional random load model was carried out. The results show that the spectrum density matrix of the synthetic multi-dimensional random load time history based on the spectrum correction method can accurately match the spectrum density matrix of the target load.