The existence of benchmark datasets is essential to objectively evaluate various image analysis methods. Nevertheless, manual annotations of fluorescence microscopy image data are very laborious and not often practicable, especially in the case of 3D+t experiments. In this work, we propose a simulation system capable of generating 3D time-lapse sequences of single motile cells with filopodial protrusions, accompanied by inherently generated ground truth. The system consists of three globally synchronized modules, each responsible for a separate task: the evolution of filopodia on a molecular level, linear elastic deformation of the entire cell with filopodia, and generation of realistic, time-coherent cell texture. The capability of our system is demonstrated by generating a synthetic 3D time-lapse sequence of a single lung cancer cell with two growing filopodia, visually resembling its real counterpart acquired using a confocal fluorescence microscope.