Quantum secure direct communication (QSDC) with the feature of allowing secret messages to be communicated directly over quantum channels has two approaches including discrete variable and continuous variable (CV). Among of them, the CVQSDC system indicates the advantages of high secrecy capacity and low experimental cost. As the number of eigenstates is unbounded, the orbital angular momentum (OAM) is an efficient method to increase the secrecy capacity in a CVQSDC system. However, OAM is very vulnerable to atmospheric turbulence, resulting in a phase distortion quantum state. In this work, we propose a CVQSDC protocol with OAM multiplexing, and reveal how the channel parameters, especially transmittance and excess noise, are influenced by atmospheric effects through the simulation experiment. On this basis, the security of the system is further analyzed and the secrecy capacity calculated. The results indicated that the increase in turbulence intensity leads to enhanced crosstalk between the OAM angular modes, which in turn leads to a decrease in the effective transmittance and an increase in the excess noise. Meanwhile, the results also showed that the secrecy capacity decreases with the increase of transmission distance, atmospheric turbulence intensity, and angular mode; in addition, OAM multiplexing can obtain more secrecy capacity compared with a single link.