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This paper deals with the following non-linear equation with a fractional Laplacian operator and almost critical exponents:
where N ⩾ 4, 0 < s < 1, (y′, y″) ∈ ℝ2 × ℝN−2, ε > 0 is a small parameter and K(y) is non-negative and bounded. Under some suitable assumptions of the potential function K(r, y″), we will use the finite-dimensional reduction method and some local Pohozaev identities to prove that the above problem has a large number of bubble solutions. The concentration points of the bubble solutions include a saddle point of K(y). Moreover, the functional energies of these solutions are in the order 
\[ (-\Delta)^{s} u=K(|y'|,y'')u^{({N+2s})/(N-2s)\pm\epsilon},\quad u > 0,\quad u\in D^{1,s}(\mathbb{R}^{N}), \]
$\epsilon ^{-(({N-2s-2})/({(N-2s)^2})}$.
