This research article primarily focuses on the method of ordinary least squares estimation of parameters of linear model. Here an innovative proof of Gauss-Markoff theorem for linear estimation has been presented. An extensive discussion in evaluating Best Linear Unbiased Estimator (BLUE) of a linear parametric function of the classical linear model is made by using the Gauss-Markoff theorem. Furthermore the importance of mean vector and covariance matrix of BLUE is discussed. Moreover generalized Gauss-Markoff theorem for linear estimation, properties of OLS estimators and problems of linear model by violating the assumptions are extensively discussed.