In an industrial power generation, power conversion is a significantly important concern. The power flow is seamless transmitted from fuel cell (FC) to electric grid through power converter components. This paper presents modelling and simulation of grid connected FC system. One of the most important types of FCs is that solid oxide fuel cell (SOFC) which has high-temperature technology, and fuel-flexible economic entitlement has been selected. The interconnection of the SOFC with a DC-DC converter and a DC-AC inverter for interfacing with the electric grid are modelled and simulated. DC-DC Boost converter is controlled by current and voltage based cascaded PI controller. Single phase adaptive filter based phase-locked loop (PLL) algorithm and pulse width modulation (PWM) is used for control of single phase DC-AC inverter. The simulation results show that the adaptive filter-PLL based control strategy is implemented for the control and synchronizing of the single phase electric grid connected SOFC system, successfully. All system components are developed by PSCAD/EMTDC simulation software.