<p>Stochastic gradient descent (SGD) method is a commonly used optimization method in machine learning. Its stepsize is a crucial factor for convergence property. The cyclic stepsize update strategy for SGD is proposed, where the approximated Cauchy step and the constant stepsize are combined. The current Cauchy step is approximated by the BB step in the next iteration. Combining with both monotone and nonmonotone linesearches, we establish the convergence results for the cyclic SGD method. The convergence analysis for different types of problems are provided. Compared to the theoretical results in literatures, the convergence assumptions for convex and strongly convex problems are weaker, where the impractical interpolation condition assumption is removed. Numerical experiments show that the proposed stepsize easily satisfies the linesearch requirement; the proposed method outperforms the benchmark methods, and enjoys the insensitivity to initialization.</p>