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 (Jup = 4–13), the C-type shock (vs = 25 km s−1, nH = 5 × 104 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⊙ yr−1). Also, our work provides SFR derivation of [C ii] from the neutral hydrogen regions only (1.38 ± 0.14 M⊙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.