High‐speed railway (HSR) is one of the most important modes of passenger transport with many advantages, such as; safety, high capacity, short intervals, and comfort. To provide high speed mobile data to the passengers of HSR for infotainment services, the best option is LTE or LTE‐R. The LTE‐R is a railway specialized network under development. The very high speed of trains in HSR, which are far faster than conventional commuters, counteracts the seamless data service and deteriorates the QoS which is mainly due to handover (HO) failure when the user equipment (UE) is moving very fast. Conventional LTE HO schemes are not designed for very high speed of HSR. Some research studies were done to provide HO schemes with more adaptation with the HSR condition but the desired specifications are not fully satisfied. In this article, we have devised a new S3 scheme for LTE HO based on time‐to‐trigger parameter in which the required ETSI's HO success rate standard at very high speed moving UE is met with a good safety margin. In addition, the presented scheme shows better performance in terms of HO latency, reference signal received power gap and handover operation probability. To do the job, an accurate mathematical analysis was developed for the proposed S3 scheme, conventional A3 and A4 schemes and the H2 scheme that we found to be the best one out of previous research studies. The results obtained have been verified by simulations.