In this paper, we study the parameter estimation problem in the system of two seemingly unrelated regressions with linear constraint. The main content contains: We prove that the covariance-adjusted constraint estimator and the constrained covariance adjustment estimator are better than the constrained least squares estimator and the covariance adjustment estimator, respectively. We define the two-stage covariance-adjusted constraint estimator and the two-stage constrained covariance adjustment estimator, and discuss their superiorities by theoretical proofs and numerical simulations. Employing the matrix power series, we obtain the estimator of regression parameter and further compare it with the limit of the sequence of the covarianceadjusted constraint estimator and the limit of the sequence of the constrained covariance adjustment estimator. For two important cases, we exhibit some interesting relationships between the limit of the covariance-adjusted constraint estimator sequence and the limit of the constrained covariance adjustment estimator sequence.