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In the framework of continuum physics, a phase field model with "ageing"-like memoryeffect is developed for a single-component material undergoing phase transition. The "ageing"-likememory effect of the phase-transition material results from the variation of the modulus of thematerial during phase transition process. To establish the phase filed model, an order parameter isintroduced to characterize the phase state of the phase-transition material in the context of the phasefield theory. In the proposed model, the order parameter is considered as an internal variable and itsevolution equation is derived via the entropy inequality. Moreover, the constitutive relations forother variables are also derived by means of the entropy inequality for the phase-transition material.To illustrate the proposed model, a specific expression for the free energy of the material isproposed, wherein the memory effect is embodied by the Stieltjes integral type strain energy of thephase-transition material. Using the expression for the free energy, the corresponding evolutionequation for the order parameter and the constitutive relations for other variables are obtained. Also,the determination of some parameters of the model is discussed in the paper briefly.