Motivated by an interest to see if the field-induced (FI) phase in the charge-density wave (CDW) system is similar to the field-induced-SDW (FISDW) in (TMTSF)2X, (TMTSF: tetramethyltetraselenafulvalene), we examined the magnetic-field-induced phases in a quasi-one-dimensional (Q1D) organic conductor HMTSF-TCNQ (hexamethylene- tetraselenafulvalene- tetracyanoquinodimethane) under a pressure of 1.1GPa, where the CDW occurring at 30K is suppressed. The work was carried out by measurements of angular-dependent magnetoresistance oscillations and exploratory work on the Hall effect. It turned out that the FI-phase, most likely a FICDWfor B > 0.1 T, accompany a quantum Hall effect, and the FI-phase transitions are controlled by the field component along the least conducting axis. Above 10 T, the lowest Landau level of the small 2D Fermi pocket (due to incomplete nesting of Fermi surface) exceeds the Fermi level, reaching the quantum limit. Although there are many differences between the CDW (HMTSF-TCNQ) and SDW ((TMTSF)2X) systems, a similar scenario for field-induced phases seems to hold.