In heavy crude oil, high viscosity exerts a large drag force on sand particles. In this paper, the influence of heavy oil viscosity on the natural settlement of sand is studied, and two models of settling velocity are established. These models have many practical applications such as calculating the time for sand to settle and designing separators and setting tanks. To visually observe and record the sand settlement process, transparent industrial white oil is used to simulate heavy oil in this study. The settling of individual particles of sand under the gravity force is experimentally studied, and drag coefficients are determined. Various models are used to predict drag coefficients of spherical and nonspherical particles, and predicted values are compared with experimental values. The results are analyzed to explore the influence of sand particle morphology on the prediction of drag coefficients. Two dimensionless settling velocity models are established and used to analyze the behavior of sand particles in heavy oil; the results prove the reliability and applicability of the settling velocity model. In this study, a nonspherical particle drag coefficient model has no advantage over a spherical particle drag coefficient model in terms of prediction accuracy. Thus, it is not necessary to consider the influence of sand particle morphology when making predictions of the characteristic parameters of sand sedimentation in heavy oil. An explicit settling velocity model is established on the basis of the Brown-Lawler drag coefficient model, and its prediction accuracy is greater than 90% for the settlement velocity of sand in heavy oil.