The binary star HD 45166 has been observed since 1922 but its orbital period has not yet been found. It is considered a peculiar Wolf-Rayet star, and its assigned classification has varied. For this reason we included the object as a candidate V Sge star and performed spectroscopy in order to search for its putative orbital period. High-resolution spectroscopic observations show that the spectrum, in emission and in absorption, is quite rich. The emission lines have great diversity of widths and profiles. The full widths at half maximum vary from 70km/s for the weakest lines up to 370km/s for the most intense ones. The Hydrogen and Helium lines are systematically broader than the CNO lines. Assuming that HD 45166 is a double-line spectroscopic binary, it present s an orbital period of P=1.596+/-0.003-day, with an eccentricity of e=0.18+/-0.08. In addition, a search for periodicity using standard techniques reveals that the emission lines present at least two other periods, of 5 and 5 hour. The secondary star has a spectral type of B7 V and, therefore, should have a mass of about M=4.8M_{sun}_. Given the radial velocity amplitudes, we determined the mass of the hot (primary) star as M=4.2+/-0.7M_{sun}_ and the inclination angle of the system, i=0.77+/-0.09deg. As the eccentricity of the orbit is non zero, the Roche lobes increase and decrease as a function of the orbital phase. At periastron, the secondary star fills its Roche lobe. The distance to the star has been re-determined as d=1.3+/-0.2kpc and a color excess of E(B-V)=0.155+/-0.007 has been derived. This implies an absolute B magnitude of -0.6 for the primary star and -0.7 for the B7 star. We suggest that the discrete absorption components (DACs) observed in the ultraviolet with a periodicity similar to the orbital period may be induced by periastron events.