Relativistic electron flux in the outer radiation belt tends to increase during the high‐speed solar wind stream (HSS) events. However, HSS events do not always cause large flux enhancement. To determine the HSS events that cause such enhancement and the mechanisms that are responsible for accelerating the electrons, we analyzed long‐term plasma data sets, for periods longer than one solar cycle. We demonstrate that during HSS events with the southward interplanetary magnetic field (IMF)‐dominant HSS (SBz‐HSS), relativistic electrons are accelerated by whistler mode waves; however, during HSS events with the northward IMF‐dominant HSS, this acceleration mechanism is not effective. The differences in the responses of the outer radiation belt flux variations are caused by the differences in the whistler mode wave–electron interactions associated with a series of substorms. During SBz‐HSS events, hot electron injections occur and the thermal plasma density decreases due to the shrinkage of the plasmapause, causing large flux enhancement of relativistic electrons through whistler mode wave excitation. These results explain why large flux enhancement of relativistic electrons tends to occur during SBz‐HSS events.