As an excellent aided communication tool, intelligent reflecting surface (IRS) can make a significant rate enhancement and coverage extension. In this paper, we present an investigation on beamforming in an IRS-aided directional modulation (DM) network. To fully explore the advantages of IRS, two beamforming methods with enhanced secrecy rate (SR) performance are proposed. The first method of maximizing secrecy rate (Max-SR) alternately optimizes confidential message (CM) beamforming vector, artificial noise (AN) beamforming vector and phase shift matrix. The first optimization vector is directly computed by the Rayleigh ratio and the last two are solved with generalized power iteration (GPI). This method is called Max-SR-GPI. To reduce the computational complexity, a new method of maximizing receive power with zero-forcing constraint (Max-RP-ZFC) of only reflecting CM and no AN is proposed. Simulation results show that the proposed two methods harvest about 30 percent rate gains over the cases of random-phase IRS and no IRS, and the proposed Max-SR-GPI performs slightly better than the Max-RP-ZFC in terms of SR, particularly in the small-large IRS.