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 astronomical thermal emission camera (AzTEC) on the Atacama Submillimeter Telescope Experiment (ASTE). We imaged a 950-arcmin2 field down to a 1{sigma} sensitivity of 0.7-1.3mJy/beam to find 125 submillimetre 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 of these SMGs with Spitzer/IRAC data and the median value is found to be z=2.4. By combining these estimations 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.