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In this letter, we propose a rank-one tensor updating algorithm for solving tensor completion problems. Unlike the existing methods which penalize the tensor by using the sum of nuclear norms of unfolding matrices, our optimization model directly employs the tensor nuclear norm which is studied recently. Under the framework of the conditional gradient method, we show that at each iteration, solving the proposed model amounts to computing the tensor spectral norm and the related rank-one tensor. Because the problem of finding the related rank-one tensor is NP-hard, we propose a subroutine to solve it approximately, which is of low computational complexity. Experimental results on real datasets show that our algorithm is efficient and effective.