Hyperbolic metamaterial (HMM), a sub-wavelength periodic artificial structure with hyperbolic dispersion, can enhance the spontaneous emission of quantum emitters. Here, we demonstrate the large spontaneous emission rate enhancement of an organic dye placed in a grating coupled hyperbolic metamaterial (GCHMM). A two-dimensional (2D) silver diffraction grating coupled with an Ag/Al2O3 HMM shows 18-fold spontaneous emission decay rate enhancement of dye molecules with respect to the same HMM without grating. The experimental results are compared with analytical models and numerical simulations, which confirm that the observed enhancement of GCHMM is due to the outcoupling of non-radiative plasmonic modes as well as strong plasmon-exciton coupling in HMM via diffracting grating.