Due to the high performance and low cost, spintronic terahertz emitters (STEs) have been a hot topic in the field of terahertz sources. However, most of the research focuses on the THz generation process and little attention has been paid to the control and modulation of the THz wave generated by the STE. In this Letter, a unidirectional spintronic terahertz emitter (USTE) integrating a common STE with a metal grating is proposed to manipulate the THz emission process. The dyadic Green's function method and finite element method are adopted to survey the characteristics of the USTE. Simulations show that the metal grating not only has a transmission larger than 97% in the optical band, but also has a higher reflectivity larger than 99% in the THz band. As a result, the USTE has a unidirectional THz emission along the direction of the pump beam with a larger than 4-fold enhancement in intensity. Moreover, the USTE has the capability of tuning the central frequency and THz wave steering by adjusting the distance and angle between the STE and the metal grating. We believe that this USTE can be used in THz wireless communications and holographic imaging, especially in the field of THz bio-sensing, which needs some resonance frequencies to sense.