We study N=1 supersymmetric SO(10) gauge theory with a field in the spinorial representation and N-f(less than or equal to 8) fields in the defining representation. It is shown that this theory for N-f=7, 8 has a dual description, which is N=1 supersymmetric SU(N-f-5) gauge theory. Its matter content for N-f=7 is different from that for N-f=8; for N-f=7, it contains 8 fields in the anti-fundamental representation. For N-f=8, a rank-2 symmetric tensor and one field in the fundamental representation appears in addition to them. This duality connects along the flat direction to the duality between the chiral and vector gauge theories discovered by Pouliot.