The problem of pedestrian collision-free navigation of self-driving cars modeled as a partially observable Markov decision process can be solved with either deep reinforcement learning or approximate POMDP planning. However, it is not known whether some hybrid approach that combines advantages of these fundamentally different solution categories could be superior to them in this context. This paper presents the first hybrid solution HyLEAP for collision-free navigation of self-driving cars together with a comparative experimental performance evaluation over the first benchmark OpenDS-CTS of simulated car-pedestrian accident scenarios based on the major German in-depth road accident study GIDAS. Our experiments revealed that HyLEAP can outperform each of its integrated state of the art methods for approximate POMDP planning and deep reinforcement learning in most GIDAS accident scenarios regarding safety, while they appear to be equally competitive regarding smoothness of driving and time to goal on average.