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In this paper, we have studied Kaluza–Klein Cosmological Model with strange-quark-matter in Lyra Geometry. To determine the solution of the field equation, we have assumed that scalar expansion is proportional to shear scalar σ 2 which leads to A 1 = (A 2) r , where A 1 , A 2 are metric potentials and r is arbitrary constant. The cosmological parameters are investigated with the help of equation of state strange-quark-matter (SQM), which is p = ρ − 4 B c 3 , where B c is Bag constant. We compared the results of general General relativity (GR) and scalar-tensor theory and also discussed the behaviors of some physical parameters. [ABSTRACT FROM AUTHOR]