The complex Monge-Ampere type equations include some of the most important partial differential equations in complex geometry and analysis. The case $\alpha = n$ corresponds to the complex Monge-Ampere equations, while for $\alpha = 1$ the equation appears in a problem proposed by Donaldson in the setting of moment maps. In this talk, I will report on the a priori estimates, and then the existence of admissible solutions. In the approach, a new Hermitian metric is constructed to launch the method of continuity.