Abstract Linear eigenmode analysis of slab ion-temperature-gradient (ITG) instabilities in weakly reversed magnetic shear configurations is performed based on a Gyro-Landau-Fluid model. Numerical results show that the linear features of the ITG instabilities are different in weakly reversed shear plasmas with double, single and non-rational surfaces, respectively. For the case with double rational surfaces separated far away, mode structures exhibit a global symmetry or antisymmetry versus the minimum of the safety factor q min with locally odd or even parity around each resonant surface. Linear properties are mainly determined by local magnetic shear as in normal magnetic shear case. With the distance between two surfaces decreasing, linear instability properties vary non-monotonically. Various high order eigenmodes are driven unstable with a moderate distance. The mode structures are eventually localized around q min surface in the single rational surface case, even nonresonant one. When there is no rational surface, the nonresonant modes are strongly driven unstable with growth rates even larger than the resonant modes. In addition, similar results in a cylinder plasma indicate the importance of non-resonant ITG instability in the short wavelength regime with weakly reversed magnetic shear.