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Recently two approaches are considered as the most promising alternatives to bulk silicon solar cells, namely, concentrator technology as well as crystalline silicon thin film (cSiTF) solar cells consisting of a thin high qual-ity epitaxial layer on top of a highly doped substrate. In the present work we made an attempt to combine these two ap-proaches and to develop concentrator solar cell based on (n+np+)Cz-Si/Al cSiTF structure, at that using Laminated Grid Cell (LGCell) design of the contact system involving transparent electrode of Indium-Fluorine-Oxide (IFO) thin film and current collecting grid made of copper wire. The epitaxial layer of n-type silicon 50 μm thick was deposited on p+-Cz-Si type substrates with resistivity of ~0.01 Ω·cm, followed by texturing, phosphorus diffusion to create FSF and screen-printing of aluminum on the back. The best cSiTF LGCell from the first run fabricated using standard LGCell process demonstrated 16.1% efficiency at 1X and 16.75% at 4X. The standard LGCell design was revisited and optimized to re-duce the series resistance. The best cSiTF cell from the second run processed using modified LGCell process showed 15.9% efficiency at 1X and 17.0% at 10X. Furthermore, conventional LGCells based on IFO/(n+pp+)Cz-Si structure made of bulk silicon were also fabricated and tested under concentrated light. Conventional cells from the first run showed 19.0% efficiency at 1X, which monotonically reduces to 18% at 4X. However in the second run we obtained the cells which showed the increase of the efficiency with concentration from 18% at 1X up to 18.3-18.5% at 3-4X.