Based on the modified Perdew and Wang exchange functional (MPW) and Becke's 1995 correlation functional (B95), we developed two hybrid meta density functional theory (HMDFT) methods, namely MPW1B95 and MPWB1K. In addition, based on the new X functional of Xin and Goddard, again combined with B95 correlation functional, we developed two other new HMDFT methods, X1B95 and XB1K. MPW1B95 and X1B95 were optimized against a representative database of six atomization energies (AE6). MPWB1K and XB1K were optimized against a kinetics database of three forward barrier heights, three reverse barrier heights, and three energies of reaction for the reactions in the BH6 representative barrier height database. We compared the newly developed methods to other HMDFT and hybrid DFT methods for atomization energies, ionization potentials, electron affinities, barrier heights, saddle point geometries, hydrogen bonding, and weak van der Waals weak interactions. In addition, we optimized scaling factors for calculating zero-point energies from vibrational frequencies. The results show that the MPWB1K and XB1K methods give good results for thermochemistry, thermochemical kinetics, hydrogen bonding, and weak interactions, and they give excellent saddle point geometries. MPW1B95 and X1B95 are suitable for general applications in thermochemistry, and they give good performance for hydrogen bonding and weak interaction calculations.