4,4′-bis[(N-carbazole) styryl] biphenyl (BSB4 or BSBCz) is one of the widely studied organic fluorescent materials for blue organic electroluminescent devices in the recent times. In this work, BSB4 is used as a guest material to construct the host-guest matrix for the emissive layer (EML) of a pure blue fluorescent organic light-emitting diode (OLED). A pure blue emission suitable for display application with a Commission Internationale de l’Eclairage (CIE) coordinate of (0.147, 0.070) is achieved by the blue-shift of the emission spectrum of the host-guest matrix from that of the pristine guest (BSB4) molecules. The optimization of OLED structures is carried out by considering (i) charge balance in the emissive layer for high exciton density, and (ii) optical interference of generated light in the organic layers for increased light outcoupling. A thorough comparative study on the use of different combinations of widely used hole and electron transport layers to obtain charge balance in the EML of the OLED, thereby enhancing the external quantum efficiency (EQE) is shown. Optical interference effects in the fabricated OLEDs are analyzed by optical simulation of each device structure by transfer matrix method (TMM). With the optimized device structures, we are able to overcome the 2% EQE limit that has been reported so far for blue fluorescent OLEDs with BSB4 as light emitting material and achieve a maximum EQE of 4.08%, which is near to the theoretical limit of EQE for fluorescent OLEDs.