To study the effect of the loading rate change on the deformation and strength properties and creep behavior of mudstone, a series of uniaxial compression tests and graded loading creep tests was conducted on mudstone specimens at four loading rates (0.005, 0.05, 0.5, and 3 mm/min). The test results find that the mudstone exhibits an obvious loading rate change effect, which is represented by an isotach viscosity behavior. When loading at a constant rate, different stress-strain relationships are observed and corresponded to different constant loading rates. When loading at variable rates, as the loading rate changes, the stress-strain relationships also change. In addition, the loading rate of mudstone prior to creep has a large impact on the creep deformation and creep rate. As the loading rate of mudstone increases before creep, the amount of creep deformation and creep rate show a gradually increasing trend. The mudstone creep rate shows a gradual decay trend over time, and the decay process can be divided into three phases: linear decay, logarithmic decay and stable decay. Furthermore, based on the three-component model and loading rate variation effect, an elasto- viscoplastic constitutive model was established. The developed constitutive model was used for the numerical modeling of mudstone laboratory tests. Compared the modeling results to the laboratory test results, it is found that the elasto-viscoplastic constitutive model can properly simulate the loading rate change effects on the mechanical properties of mudstone under uniaxial compression conditions.