An analytical approach is presented to evaluate the Bit Error Rate (BER) performance of a multicore fiber (MCF) communication system with On-Off Keying (OOK) modulation scheme. The expressions of the signal power at the output of the different cores of the MCF with excitation to any one of the cores is found out along with the crosstalk due to coupling among the cores. Finally, the expression for Signal to Crosstalk Ratio (SCR) at the output of the excited fiber core is found. The BER for a given data rate is then determined numerically for different MCF parameters and transmission distance. The outcome of this research work will be useful to design fiber optic system with Multi-core Multi-mode fiber running at BER comparable to single mode fiber links.