The generalized integral Fourier transform \begin{gather*}
\widetilde{f}(\alpha)=\frac{1}{\sqrt{2\pi}}\int\limits_{-\infty}^{\infty}
f(x)e^{i{\alpha}x}{_{1}\Phi^{\tau,\beta}_{1}}(a;c;-r({\alpha}x))\,dx,
\end{gather*}
where $\rm{Re}\,\it{c}> \rm{Re}\,\it{a}>0$, $ ({\tau,\beta})\subset R $, $ \tau-\beta<1$, $r>0$, and  ${{_{1}\Phi}^{\tau,\beta}_{1}}(\ldots )$ is the $(\tau,\beta)$-confluent hypergeometric function, is introduced. The inversion formula of this integral transform is proved. The basic properties of a new integral Fourier transform and some examples are given.