In many clinical studies, Lin’s concordance correlation coefficient (CCC) is used to assess the agreement of a continuous response measured by two raters or methods. However, the need for measures of agreement may arise for more complex situations, such as when the responses are measured on more than one occasion by each rater or method. We propose a new CCC in the presence of multivariate or repeated measurements data, called the matrix-based concordance correlation coefficient (MCCC). For inference, we propose an estimator based on U-statistics. We derive the asymptotic normality of the estimator. Simulation studies confirm that overall in terms of accuracy, precision, and coverage probability, the estimator of the MCCC works very well in general cases especially when n is greater than 40. We present two examples to illustrate the methodology.