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Purpose – In this paper, the authors prove that the Douglas space of second kind with a generalised form of special (α, β)-metric F, is conformally invariant. Design/methodology/approach – For, the authors have used the notion of conformal transformation and Douglas space. Findings – The authors found some results to show that the Douglas space of second kind with certain (α, β)-metrics such as Randers metric, first approximate Matsumoto metric along with some special (α, β)-metrics, is invariant under a conformal change. Originality/value – The authors introduced Douglas space of second kind and established conditions under which it can be transformed to a Douglas space of second kind.