The all sky monitor (ASM) on board Ginga discovered an X-ray outburst from the recurrent X-ray pulsar, X0115 + 634, on 1990 February 5. The maximum intensity of about 400 mcrab (1-20 keV) occurred around February 11. We have determined an intrinsic pulse period of 3.614690 +/- 0.000002 s as well as the orbital parameters. By combining the present results with previous ones obtained with other satellites, we can study the evolution of the orbital parameters. In particular, we have determined the apsidal motion of the orbit, omega = 0-degrees-.030 +/- 0-degrees-.016 yr-1 (95% confidence). This determination places constraints on the mass-radius relation of the Be companion. An X-ray spectrum up to 60 keV was obtained with the LAC. We confirmed two absorption-line features that are cyclotron resonance lines originating from a magnetic source with field strength of 1 x 10(12) G and magnetic dipole moment, mu, of 1 x 10(30) G cm-3. Timing data obtained when the source was faint could not be connected with timings at a higher intensity, suggesting a change in the pulse shape. Based on our estimate of mu, the source was then near the critical accretion luminosity, L(crit), below which a "propeller" effect becomes effective.