We are concerned with the following fractional elliptic equation with almost critical non-power non-linearity \(\begin{aligned} \left\{ \begin{array}{lll} (-\Delta )^s u =\frac{|u|^{2_s^*-2}u}{[\ln (e+|u|)]^\varepsilon }\ \ & \textrm{in}\ \Omega , \\ u= 0 \ \ & \textrm{on}\ \partial \Omega , \end{array} \right. \end{aligned}\) where \(\Omega \) is a bounded smooth domain in \(\mathbb {R}^n\) with \(n\ge 2\,s+1\) , \(s\in (\frac{1}{2},1)\) , \((-\Delta )^s\) is the spectral fractional Laplacian operator with zero Dirichlet boundary condition, \(2_s^*=\frac{2n}{n-2s}\) is the fractional critical Sobolev exponent, \(\varepsilon >0\) is a small parameter. By employing the Lyapunov-Schmidt reduction argument, we prove that this problem admits a sign-changing solution behaving like a superposition of bubbles blowing-up at minimum points of the Robin function with different rates of concentration as \(\varepsilon \) goes zero.
