An effective method is presented for using generalized orthogonal polynomials (GOP) for identifying the parameters of a process whose behaviour can be modelled by a linear differential equation with time-invariant coefficients. The method is based on the differentiation operational matrix of the GOP, which can represent all kinds of individual orthogonal polynomials. The main advantage of using the differentiation operational matrix is that parameter estimation can be made starting at any time of interest, without the restriction of starting at zero time. Using the concept of GOP expansion for a state function and a control function, the differential input-output equation is converted into a set of over-determined linear algebraic equations. The unknown parameters are evaluated by a weighted least-squares estimation method. Two examples are given to demonstrate the validity of the method and good results are obtained.