<p>In this paper, we investigate a test for parameter instability with an unknown change point in the low-rank tensor regression model. Assuming the tensor coefficient admits the CP decomposition, we embed the low-rank structure into the tensor regression, ensuring structural preservation and computational feasibility. To estimate the parameters, we construct the full-sample and partial-sample OLS estimators and prove their consistency under the null hypothesis. Based on these, we propose the quasi-likelihood ratio test statistic for detecting non-stationarity and derive its asymptotic distribution under the null hypothesis as the supremum of the square of a standardized tied-down Bessel process. Additionally, we explore the asymptotic local power under local alternatives, demonstrating that our test is a powerful tool for structural change detection. The results of simulation studies and empirical applications confirm the efficiency of the proposed method.</p>