<p>In this article, we propose a testing procedure for detecting the inequality of covariance functions between two-samples of large-scale functional data. The asymptotic null distribution of the test statistic is established under mild conditions, and the power of the test is shown to be consistent under quite general alternatives. The proposed test benefits from several advantages that distinguish it from the conventional framework of functional data analysis. The first advantage is named as “eigenvalue-decay-free” since none of the conditions are imposed on the decaying pattern of the eigenvalues of each functional data. The second advantage is regarded as “square-integrable-free” since we do not require any functional data to be square-integrable. Other advantages include, but are not limited to, the permission of ultra-high-dimensionality, fairly different sample sizes, and non-Gaussian functional observations. We evaluate the numerical performance of the proposed test by a simulation study as well as a real data application.</p>