Abstract: We considered the existence of solutions of differential equations for fractional Choquard type Kirchhoff critical problems. Firstly, Hardy-Littlewood-Sobolev embedding theorem was introduced, and combined with Nehari manifold method and fibbing maps of energy functional related to the problem, the existence of nontrivial solution of the equation was proved when the parameter λ was small enough. Secondly, the functional had (PS) sequence was obtained by Ekeland variational principle, and then the appropriate parameter λ was selected. Combined with the truncation method and mountain pass theorem, the compactness 
condition was proved to be true. Finally, the existence of nontrivial solutions of the above equations was established by using the fractional concentration-compactness principle.

Key words: Choquard equations, fractional, critical exponent, Hardy-Littlewood-Sobolev inequality, nontrivial solution