We present the Submillimeter Array (SMA) observation of the CO J = 2-1 transition toward the northern galaxy, ARP 302N, of the early merging system, ARP 302. Our high angular resolution observation reveals the extended spatial distribution of the molecular gas in ARP 302N. We find that the molecular gas has a very asymmetric distribution with two strong concentrations on either side of the center together with a weaker one offset by about 8 kpc to the north. The molecular gas distribution is also found to be consistent with that from the hot dust as traced by the 24 μm continuum emission observed by Spitzer. The line ratio of CO J = 2-1/1-0 is found to vary strongly from about 0.7 near the galaxy center to 0.4 in the outer part of the galaxy. Excitation analysis suggests that the gas density is low, less than 10³ cm^–3, over the entire galaxy. By fitting the spectral energy distribution of ARP 302N in the far infrared we obtain a dust temperature of T _d = 26-36 K and a dust mass of M _dust = 2.0-3.6 × 10⁸ M . The spectral index of the radio continuum is around 0.9. The spatial distribution and spectral index of the radio continuum emission suggest that most of the radio continuum emission is synchrotron emission from the star-forming regions at the nucleus and ARP 302N-cm. The good spatial correspondence between the 3.6 cm radio continuum emission, the Spitzer 8 and 24 μm data and the high-resolution CO J = 2-1 observation from the SMA shows that there is asymmetrical star-forming activity in ARP 302N.