Spin gapless semiconductors (SGS) form a new class of magnetic semiconductors, which has a band gap for one spin sub band and zero band gap for the other, and thus are useful for tunable spin transport based applications. In this paper, we report the first experimental evidence for spin gapless semiconducting behavior in CoFeMnSi Heusler alloy. Such a behavior is also confirmed by first principles band structure calculations. The most stable configuration obtained by the theoretical calculation is verified by experiment. The alloy is found to crystallize in the cubic Heusler structure (LiMgPdSn type) with some amount of disorder and has a saturation magnetization of 3.7 Bohrs magneton/f.u.. and Curie temperature of 620 K. The saturation magnetization is found to follow the Slater-Pauling behavior, one of the prerequisites for SGS. Nearly temperature-independent carrier concentration and electrical conductivity is observed from 5 to 300 K. An anomalous Hall coefficient of 162 S/cm is obtained at 5 K. Point contact Andreev reflection data has yielded the current spin polarization value of 0.64, which is found to be robust against the structural disorder. All these properties are quite promising for the spintronic applications such as spin injection and can bridge a gap between the contrasting behavior of half-metallic ferromagnets and semiconductors.