Friction is an important part of many dynamic systems, and, as a result, a good model of friction is necessary for simulating and controlling these systems. A new friction model, designed primarily for optimal control and real-time dynamic applications, is presented in this paper. This new model defines friction as a continuous function of velocity and captures the main velocity-dependent characteristics of friction: the Stribeck effect and viscous friction. Additional phenomena of friction such as microdisplacement and the time dependence of friction were not modeled due to the increased complexity of the model, leading to reduced performance of real-time simulations or optimizations. Unlike several current friction models, this model is C1 continuous and differentiable, which is desirable for optimal control applications, sensitivity analysis, and multibody dynamic analysis and simulation. To simplify parameter identification, the proposed model was designed to use a minimum number of parameters, all with physical meaning and readily visible on a force–velocity curve, rather than generic shape parameters. A simulation using the proposed model demonstrates that the model avoids any discontinuities in force at initial impact and the transition from slipping to sticking.