Tensile creep is an important factor affecting the early cracking resistance of concrete. The tensile creep model can effectively predict the development of tensile creep. In order to establish an appropriate tensile creep model, a temperature–stress testing machine (TSTM) was employed to test the development of temperature, deformation and restraint stress of benchmark concrete and concrete mixed with the MgO under different temperature curing modes. The development law of early age stress, strain and creep was analyzed via the test data of the TSTM. The early age tensile creep of concrete was predicted with the existing Kelvin creep model. The effect of variable temperature on creep was considered in this study, and an improved Kelvin creep model was proposed. The prediction accuracy of the two models was compared and analyzed. The results indicate that MgO has little influence on the creep and specific creep of concrete. The early age cracking resistance of MgO concrete is better than benchmark concrete. The improved Kelvin model based on the microprestress-solidification (MPS) theory predicts the early tensile creep of concrete more accurately in variable temperature conditions. These are significantly helpful for the application of the MgO expansion agent in dam engineering.