This article considers a novel intelligent reflecting surface (IRS)-assisted cell-free symbiotic radio (SR) system, where an IRS is employed to facilitate the transmission from all the base stations (BSs) to the primary receivers (PRs), i.e., the primary transmission, and simultaneously, to send messages to the Internet of Things (IoT) devices, i.e., the secondary transmission. We aim to minimize the bit error rate (BER) of the IRS symbols by jointly optimizing the transmit beamformers at all the BSs and the IRS phase shifts. To solve this nonconvex problem, we propose a plenty-based algorithm by using the multidimensional complex quadratic transform (MCQT) and the consensus alternative direction method of multipliers (ADMMs) methods, and obtain a high-performance solution. Besides, the convergence of the proposed algorithm is analyzed. Simulation results demonstrate the effectiveness of the proposed algorithm and show that the proposed algorithm outperforms two baselines under different setups.