The effect of doping non Jahn-Teller (JT) Cr³⁺ ion on the crystallographic structure and magnetic ordering has been studied in a series of polycrystalline compounds HoMn_1−xCr_xO₃ (0 < x≤1). These compounds crystallize in a mixture of hexagonal and orthorhombic phases for x < 0.125 whereas the orthorhombic phase is present for all higher concentrations. It is observed that Cr doping leads to decrease in the mismatch of the bond length in Mn-O₆ octahedra indicating reduction in the static orbital ordering due to JT effect. In addition, doping with Cr³⁺ introduces ferromagnetic Mn³⁺-O-Cr³⁺ interactions in an antiferromagnetic matrix consisting of Mn³⁺-OMn³⁺ and Cr³⁺-O-Cr³⁺ interactions. A change in the magnetic structure from Г₄ (A_xF_yG_z) to Г₂ (C_xG_yF_z) is observed in samples with x > 0.75, which is attributed to the anisotropic interactions between the Ho³⁺ and Cr³⁺ spins. An incommensurate magnetic order corresponding to the wave vector (0.4, 0, 0) is observed in the orthorhombic phase associated with the x=0.05 sample. The hexagonal phase in the Mn-rich end exhibits a reduced magnetic ordering temperature of 55 K and a spin reorientation at 15 K, in comparison to h-HoMnO₃.The temperature variation of dielectric data shows weak magnetodielectric coupling in these compounds.