As a promising technology, free-space optical (FSO) communication plays an important role in the next generation of wireless communication. A dual-hop FSO communication system with decode-and-forward (DF) protocol is proposed in this paper, considering the influences of the atmospheric turbulence (AT), atmospheric absorption and pointing error impairments, in which the Málaga distribution model is used to characterize the fading caused by AT in each link. The end-to-end statistical expressions of our proposed dual-hop Málaga-Málaga communication system are derived, such as the cumulative distribution function (CDF), probability density function and moment generating function. Thereafter, using the above statistical results, the accurate endto-end expressions of outage probability, average bit error rate (ABER) and ergodic capacity are deduced under the direct detection intensity modulation and heterodyne detection techniques. Furthermore, the end-to-end asymptotic expressions for CDF and the ABER at high signal-to-noise ratio as well as simplified expressions from simple basic functions are obtained. The effects of different AT and pointing error impairments conditions on the proposed system are analyzed based on theoretical and numerical results. Finally, Monte Carlo simulation results indicate that all our novel deduced expressions are basically consistent with the numerical results.