In the present study, to characterize material behavior of an ammonium perchlorate - hydroxyl terminated polybutadiene (AP-HTPB) base composite solid propellant, tension tests were performed with various temperatures and strain rates. Stress relaxation tests were also carried out at various temperatures to determine the tensile modulus of the material. In addition to these tests, three types of cyclic tests and dilatation test were carried out to identify the effect of internal damage evolution to the material response. From the results of three cyclic tests, Mullins effect was observed, and from the dilatation test, volumetric damage incurred by de-bonding between the filler and matrix material was observed as well. Based on such findings, a viscoelastic constitutive modeling with the Mullins effect and damage is proposed. Numerical simulations with the newly proposed damage model reproduced the experimental findings at various test conditions fairly well. It was found out that the proposed viscoelastic constitutive model could be used to efficiently characterize the material response of the solid propellant depending on various strain rates and temperatures according to the present study.