The average bit error rate (ABER) performance of low-density parity-check (LDPC)-coded orthogonal frequency-division multiplexing (OFDM) free-space optical communication system with K-ary quadrature amplitude modulation (QAM) and phase shift keying (PSK) modulation schemes is investigated over the composite Málaga fading channel with atmospheric attenuation and pointing errors considered. The probability density function and cumulative distribution function regarding the aggregated channel model are derived with the help of the generalized Gauss-Laguerre quadrature rule, the analytical ABER expressions for both QAM and PSK OFDM systems are then obtained. On the basis of them, the ABER performance is analyzed with different turbulence strengths, weather conditions, normalized beam width, normalized jitter, and specifically, different values of Málaga distribution parameter ρ. Monte Carlo simulation is offered to confirm the correctness of the proposed ABER models. Moreover, LDPC codes are added into the simulation to enhance system performance. The result shows that, for the same turbulence, weather, and pointing error conditions, whether the LDPC codes are taken into account or not, the ABER performance of 16-QAM OFDM system is better than that of 16-PSK OFDM system over the Málaga fading channel, and the ABER result decreases with higher ρ for both modulation schemes. Furthermore, the LDPC coding can significantly improve the system performance over this aggregated fading channel for these two modulation schemes, and a lower LDPC code rate can obtain a better ABER performance. This work is beneficial for free-space optical system design.