The lithospheric magnetic field is an important component of the geomagnetic field, and the oceanic lithosphere exhibits distinct characteristics. Because of its formation mechanisms, evolutionary history, and geomagnetic field polarity reversals, the oceanic lithosphere has significant remanent magnetization, which causes magnetic anomaly stripes parallel to the mid-ocean ridges. However, it is difficult to construct a high-resolution lithospheric magnetic field model in oceanic regions with relatively sparse data or no data. Using forward calculated lithospheric magnetic field data based on an oceanic remanent magnetization (ORM) model with physical and geological foundations as a supplement is a feasible approach. We first collect the latest available oceanic crust age grid, plate motion model, geomagnetic polarity timescale, and oceanic lithosphere thermal structure. Combining the assumptions that the paleo geomagnetic field is a geocentric axial dipole field and that the normal oceanic crust moves only in the horizontal direction, we construct a vertically integrated ORM model of the normal oceanic crust with a known age, including the intensity, inclination, and declination. Both the ORM model and the global induced magnetization (GIM) model are then scaled from two aspects between their forward calculated results and the lithospheric magnetic field model LCS-1. One aspect is the difference in their spherical harmonic power spectra, and the other is the misfit between the grid data over the oceans. We last compare the forward calculated lithospheric magnetic anomaly from the scaled ORM and GIM models with the Macau Science Satellite-1 (MSS-1) observed data. The comparison results show that the magnetic anomalies over the normal oceanic crust regions at satellite altitude are mainly contributed by the high-intensity remanent magnetization corresponding to the Cretaceous magnetic quiet period. In these regions, the predicted and observed anomalies show good consistency in spatial distribution, whereas their amplitude differences vary across regions. This result suggests that regional ORM construction should be attempted in future work to address these amplitude discrepancies.