We present the results from a 1.1 mm imaging survey of the SSA22 field, known for having an overdensity of z=3.1 Lyman-alpha emitting galaxies (LAEs), taken with the AzTEC camera on the Atacama Submillimeter Telescope Experiment (ASTE). We imaged a 950 arcmin$^2$ field down to a 1 sigma sensitivity of 0.7-1.3 mJy/beam to find 125 submillimeter galaxies (SMGs) with a signal to noise ratio >= 3.5. Counterpart identification using radio and near/mid-infrared data was performed and one or more counterpart candidates were found for 59 SMGs. Photometric redshifts based on optical to near-infrared images were evaluated for 45 SMGs of these SMGs with Spitzer/IRAC data, and the median value is found to be z=2.4. By combining these estimation with estimates from the literature we determined that 10 SMGs might lie within the large-scale structure at z=3.1. The two-point angular cross-correlation function between LAEs and SMGs indicates that the positions of the SMGs are correlated with the z=3.1 protocluster. These results suggest that the SMGs were formed and evolved selectively in the high dense environment of the high redshift universe. This picture is consistent with the predictions of the standard model of hierarchical structure formation.