It is well known that monolayer transition-metal dichalcogenides (MX2, M = Mo, W and X = S, Se, Te) could exist in three common structures, i.e. 1T, 1 T', and 1H phases. In order to reveal their possible phase transitions driven by biaxial strain, we use first-principles calculations to determine the energy landscapes associated with these three phases. Due to its intrinsic dynamical instability, the centrosymmetric 1T phase is known to be metastable and will transform into the 1T' phase where pairs of metal atoms pull together toward each other. Moreover, controlling the metallic 1T' and semiconducting 1H phases is of particular interest as this can introduce novel opportunities in a series of applications. When a biaxial strain is simultaneously compressed along the zigzag direction and stretched along the armchair direction, phase transitions from 1H to 1T' have occurred in MSe2 and MoTe2, but for MSe2 the biaxial strain is much difficult to realize in experiments. For WTe2, the 1 T' structure will transform into the 1H form when a biaxial strain is just compressed along the armchair direction. The transitions between 1H and 1T' phases could be attributed to the changes of metal-chalcogen bonds along the armchair direction by analyzing the Crystal Orbital Hamilton Population. Only half M-X bonds along the armchair direction is the main factor, because their lengths are robust in 1T' phase and decrease in 1H form with the tensile strain applied along the armchair direction. Our findings provide a guideline for the phase engineering of transition-metal dichalcogenides with biaxial strain.