In this paper, a novel dual-hop relay-assisted hybrid Free Space Optical / Radio Frequency (FSO / RF) communication system is presented. In this structure an access point connects users within the building to the Base Station via a hybrid parallel FSO / RF link, this link is proposed firstly. Parallel combination of FSO and RF links and use of an access point, will increase capacity, reliability and data rate of the system. It is the first time that the effect of number of users on the performance of a dual-hop relay-assisted hybrid parallel FSO / RF system is investigated. FSO link is considered in Gamma-Gamma atmospheric turbulence with the effect of pointing error and RF link is considered in Rayleigh fading. For the first time, closed-form expressions are derived for Bit Error Rate (BER) and Outage Probability (P_out) of the proposed system. Derived expressions are verified through MATLAB simulations. It is shown that the performance of the proposed system is almost independent of atmospheric turbulence intensity, thereby when atmospheric turbulence strengthens, low power consumption is required for maintenance of the system performance. Hence the proposed structure is particularly suitable for mobile communication systems in which a small mobile battery supplies transmitter power. Also the proposed system performance of the system is preferable even at low signal to noise ratio (SNR). Therefore, proposed structure significantly reduces power consumption while maintaining performance of the system.