Model predictive controller (MPC) has demonstrated its competency in controlling autonomous vehicles. But to apply the current MPC-based schemes, it has to be formulated into certain formats and meet all prerequisites in order to fit the optimization solvers. To eliminate the gaps, in this paper, we propose a nonlinear MPC controller which controls the vehicle velocity and steering simultaneously. The optimization solver is based on genetic algorithms (GA). As compared to other solvers, using GA in the optimization enables a more flexible structure for MPC formulation. The cost function and constraints can be designed in a more accurate, meaningful, and direct way. Both simulation and on-field test results showed that the vehicle under the control of the proposed nonlinear MPC is able to follow the road center line accurately and consistently, even at sharp corners. Moreover, the results also showed that passengers' safety and comfort can be well taken care of under the proposed MPC scheme as both the vehicle movement acceleration and steering acceleration are well confined within a safety range. The promising results indicate that the proposed GA-based nonlinear MPC can be a suitable solution to autonomous vehicle control.