This paper describes the method of approximating the desired variable characteristics by a transfer function containing one kind of variable parameter in consideration of minimal realization. We propose two new models of the approximating variable transfer function which is minimally realizable. In the conventional model considering minimal realization, the poles are independent of the variable parameter \(\lambda\), while in our ones both the poles and zeros depend on \(\lambda\). Consequently, they can represent a wider range of the variable characteristics. Making use of the property that the approximating transfer function is minimally realizable, we also present the method of improvement of the approximation accuracy for the specified value of \(\lambda\) by use of Markov parameters.