The Tensor-Product (TP) model transformation is a recently proposed numerical method capable of transforming linear parameter varying state-space models to the Higher Order Singular Value Decomposition (HOSVD) based canonical form of polytopic models. It is also capable of generating various types of convex TP models as well for linear matrix inequality based control design. The crucial point of the TP model transformation is that its computational load exponentially explodes with the dimensionality of the parameter vector of the state-space model. In this paper we propose a modified TP model transformation that computes the HOSVD-based canonical form by dimensionality reduced sub-spaces of the parameter vector that leads to the considerable reduction of the computation. A numerical example is also given to show how the modified TP model transformation can readily be executed in cases when the original TP model transformation fails.