In this paper, a novel directional modulation (DM) network utilizing the distributed active intelligent reflecting surface (IRS) to enhance the secrecy sum-rate (SSR) performance is established, with each unmanned aerial vehicle (UAV) hanging an IRS. The degree of freedom (DoF) is only two in the single-IRS-aided DM network, which will seriously limit its rate performance. Multiple active IRSs will create more DoFs for DM network and dramatically enhance its rate. Three IRS-user matching methods, path loss coefficient (PLC) matching, distance matching, and signal-to-interference-plus-noise ratio (SINR) matching, are proposed to enhance the SSR performance, where all IRSs are equipartitioned into two parts, one part is matched to Bob and the other part to Eve. The double layer leakage (DLL) and minimum-mean square error (MMSE) rules, called DLL-MMSE, are adopted to construct beamforming at transmitter, IRS and receiver, respectively. The double layer null-space projection (DLNSP), Rayleigh ratio (RR) and MMSE schemes, called DLNSP-RR-MMSE, are used to acquire the transmit beamforming vector, phase shift matrix (PSM) and receive beamforming vector, respectively. Simulation results show that the proposed SINR matching scheme outperforms the remaining two ones in terms of SSR. It is also verified that a significant SSR enhancement over single IRS is achieved by using multiple distributed IRSs.