High resolution angle resolved photoemission measurements and band structure calculations are carried out to study the electronic structure of BaMnSb2.All the observed bands are nearly linear that extend to a wide energy range.The measured Fermi surface mainly consists of one hole pocket around F and a strong spot at Y which are formed from the crossing points of the linear bands.The measured electronic structure of BaMnSb2 is unusual and deviates strongly from the band structure calculations.These results will stimulate further efforts to theoretically understand the electronic structure of BaMnSb2 and search for novel properties in this Dirac material.