Magnetization induced optical second harmonic generation is used to investigate the surface magnetic properties during the layer-by-layer growth of Co films on Cu(001). The second harmonic (SH) signal changes as a function of Co thickness and an oscillatory behavior of the SH asymmetry with one monolayer period is observed for the transverse Kerr-geometry and s-polarized incident light, while the average SH signal has no such oscillations. The magnetization induced SH signal at half filled layers is enhanced with respect to that of filled layers, which agrees with the enhancement of magnetic moment of edge atoms and the higher step density at half filled layers. Its dependences on the growth rate and temperature are discussed.