NGC 1266 is a lenticular galaxy (S0) hosting an active galactic nucleus (AGN), and known to contain a large amount of shocked gas. We compare the luminosity ratio of mid-J CO lines to IR continuum with star-forming galaxies (SFGs), and then model the CO spectral line energy distribution (SLED). We confirm that in the mid- and high-J regions (J (up) = 4-13), the C-type shock (v (s) = 25 km s(-1), n (H) = 5 x 10(4) cm(-3)) can reproduce the CO observations well. The galaxy spectral energy distribution (SED) is constructed and modeled by the code X-CIGALE and obtains a set of physical parameters including the star formation rate (SFR, 1.17 +/- 0.47 M (circle dot) yr(-1)). Also, our work provides SFR derivation of [C ii] from the neutral hydrogen regions only (1.38 +/- 0.14 M (circle dot)yr(-1)). Previous studies have illusive conclusions on the AGN or starburst nature of the NGC 1266 nucleus. Our SED model shows that the hidden AGN in the system is intrinsically low-luminosity, consequently the infrared luminosity of the AGN does not reach the expected level. Archival data from NuSTAR hard X-ray observations in the 3-79 keV band shows a marginal detection, disfavoring presence of an obscured luminous AGN and implying that a compact starburst is more likely dominant for the NGC 1266 nucleus.