An accurate MGGA-based hybrid exchange-correlation functional is proposed based on Becke's exact mixing approach. The presented functional makes use of the exact E-x and meta-generalized gradient approximations (MGGAs) to E-xc containing local density, gradient, Laplacian, and kinetic energy density and is tested on 19 atomization energies. The results show that this functional, which contains only one parameter fit to atomization energies of molecules, improves or competes with the previously proposed accurate hybrid functionals in the literature for atomization energies of the molecules we tested, with an impressively small mean absolute error (mae) of 1.3 kcal/mol. This suggests that chemical accuracy may be achieved within Kohn-Sham density functional formalism without the use of many parameters fitted to atomization energies.