We studied the Fermi surface of the organic conductor (TMTSF)2NO3 through the measurements of magnetic quantum oscillations. Well defined Shuvnikov-de Haas(SdH) oscillations with frequency of ca. 60T can be observed below 8K and above 6T at the ambient pressure. Under a pressure of 8kbar, different oscillations with frequency of ca. 180T is observed above 10T at 450mK. Electron structure at low temperature seems strongly modified upon application of pressure which may explain the absence of superconductivity and the field-induced spin-density waves. The angular magnetoresistance could not be fit neither by Yamaji's model nor by Lebed's.