The main purpose of this paper is to discuss novel fractional wavelet frame (NFRWF), which is based on fractional Fourier transform of novel fractional wavelet system. By analyzing Fourier transformation of the \(\alpha \) -order novel fractional wavelets, we obtain some necessary and sufficient conditions for \(\{\psi _{\alpha ,j,k}\}_{j,k\in \mathbb {Z}}\) to be NFRWF in \(L_2(\mathbb {R})\) . Further, a necessary and sufficient condition is given for \(\{\psi _{\alpha ,j,k}\}_{j,k\in \mathbb {Z}}\) to be tight NFRWF, when in a special case the parameters are selected as \(a_0 = 2\) and \(b_0 = 1\) in \(\{\psi _{\alpha ,j,k}\}_{j,k\in \mathbb {Z}}\) .