A basis-based speaker adaptation technique is proposed, where basis vectors are derived using two-dimensional principal component analysis (2DPCA) and the speaker weight for the target speaker is constrained in the space of training speaker weights. During adaptation, the speaker weight that is derived in the maximum-likelihood framework is constrained by projecting the weight into the space of the weights of training speakers. In the experiments, the proposed approach shows performance improvement over the unconstrained 2DPCA-based approach.