In this Letter we present the detection, for the first time, of double-peaked broad Balmer H-alpha and H-beta emission-line profiles in a luminous IRAS galaxy: IRAS 02366-3101 with log L(FIR) = 10.94 L.. These double-peaked broad emission-line profiles consist of three components characterized by the following mean parameters: (1) a narrow component with FWHM = 571 km s-1, (2) a blueward broad component with FWHM = 2794 km s-1 and velocity shift of the peak of -2120 km s-1, (3) a redward broad component with FWHM = 2614 km s-1 and velocity shift of the peak of +2911 km s-1, and (4) a blueward broad-to-redward broad emission-peak ratio of around 1.2. These parameters are consistent with the emission-line profile predicted by models such as those of Chen and Halpern, where the low-ionization line emission comes from a relativistic accretion disk around a supermassive black hole. This detection shows that IRAS 02366-3101 is a candidate to host an accretion disk around a supermassive black hole in its nucleus, although other alternatives cannot be ruled out.