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We consider the following fractional problem involving slightly subcritical non‐power nonlinearity, (−Δ)su=|u|2s∗−2u[ln(e+|u|)]εinΩ,[2mm]u=0on∂Ω,$$\begin{equation*} {\hspace*{60pt}\left\lbrace \def\eqcellsep{&}\begin{array}{lll}(-\Delta)^s u =\frac{|u|^{2_s^*-2}u}{[\ln (e+|u|)]^\epsilon }\ \ &{\rm in}\ \Omega, [2mm] u= 0 \ \ & {\rm on}\ \partial \Omega, \end{array} \right.} \end{equation*}$$where Ω$\Omega$ is a smooth bounded domain in Rn$\mathbb {R}^n$, n≥2s+1$n\ge 2s+1$, s∈(12,1)$s\in (\frac{1}{2},1)$, 2s∗=2nn−2s$2_s^*=\frac{2n}{n-2s}$ is the fractional critical Sobolev exponent and ε>0$\epsilon >0$ is a small parameter, (−Δ)s$(-\Delta)^s$ is the spectral fractional Laplacian operator. We construct a positive bubbling solution, which concentrates at a nondegenerate critical point of the Robin function by Lyapunov–Schmidt reduction procedure. [ABSTRACT FROM AUTHOR]