The advent of sensitive low frequency radio observations has revealed a number of diffuse radio objects with peculiar properties that are challenging our understanding about the physics of the intracluster medium. Here, we report the discovery of a steep spectrum radio halo surrounding the central Brightest Cluster Galaxy (BCG) in the galaxy cluster SPT-CL J2031-4037. This cluster is morphologically disturbed yet has a weak cool core, an example of cool core/non-cool core transition system, which harbours a radio halo of $sim 0.7$ Mpc in size. The halo emission detected at 1.7 GHz is less extended compared to that in the 325 MHz observation, and the spectral index of the part of the halo visible at 325 MHz to 1.7 GHz frequencies was found to be $-1.35 pm 0.07$. Also, $P_{1.4 mathrm{GHz}}$ was found to be $0.77 times 10^{24}$ W Hz$^{-1}$ which falls in the region where radio mini-halos, halo upper limits and ultra-steep spectrum (USS) halos are found in the $P_{1.4 mathrm{GHz}} - L_mathrm{X}$ plane. Additionally, simulations presented in the paper provide support to the scenario of the steep spectrum. The diffuse radio emission found in this cluster may be a steep spectrum intermediate or hybrid radio halo which is transitioning into a mini-halo.
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