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An approximate model predictive control approach is applied on an unmanned aerial vehicle with limited computational resources. A novel method using a continuous time parametrization of the state and input trajectory is used to derive a compact description of the optimal control problem. Different first order methods for the online optimization are discussed in terms of memory requirements and execution time. The generalized fast dual gradient method is implemented on the aerial vehicle. The approximate model predictive control algorithm runs on an embedded platform with a STM32 Cortex M4 processor. Simulation studies show that the model predictive controller outperforms a linear quadratic regulator in aggressive maneuvers. The model predictive control approach is evaluated in practice and shown to yield satisfactory flight behavior.