Samejima ("Psychometrika "65:319--335, 2000) proposed the logistic positive exponent family of models (LPEF) for dichotomous responses in the unidimensional latent space. The objective of the present paper is to propose and discuss a graded response model that is expanded from the LPEF, in the context of item response theory (IRT). This specific graded response model belongs to the general framework of graded response model (Samejima, "Psychometrika Monograph," No. 17, 1969 and No. 18, 1972; "Handbook of modern item response theory," Springer, New York, 1997; "Encyclopedia of Social Measurement," Academic Press, San Diego, 2004), and, in particular to the heterogeneous case (Samejima, "Psychometrika Monograph," No. 18, 1972). Thus, the model can deal with any number of ordered polytomous responses, such as letter grades (e.g., A, B, C, D, F), etc. For brevity, hereafter, the model will be called the LPEF graded response model, or LPEFG. This model reflects the opposing two principles contained in the LPEF for dichotomous responses, with the logistic model (Birnbaum, "Statistical theories of mental test scores," Addison Wesley, Reading, 1968) as their transition, which provide a reasonable rationale for partial credits in LPEFG, among others.