Diffraction of the $H$-polarized electromagnetic wave by a semi-infinite strip grating is considered. The scattered field is represented as a superposition of the field induced by the currents on the strips of an infinite periodic grating and the field induced by the correction current excited due to end of the grating. Singular integral equations with additional conditions for infinite and semi-infinite periodic gratings are obtained. The current on the strips and spectral function of scattered field are expressed in terms of the solution of these equations. Numerical results for the near and far fields distribution are represented.