In this paper, four-dimensional real Lie groups with left-invariant Riemannian metrics and a harmonic concircular curvature tensor are investigated. This is a continuation of the researches of authors on three-dimensional Lie groups with left-invariant Lorentz’s metric, and a harmonical concircular curvature tensor. Concircular transformations (i.e. non-trivial conformal transformations that transform the geodesic circles in the geodesic circles) and one of their invariants – concircular curvature tensor were introduced by K. Yano. Their importance in the geometry of F-structures such as complex, almost complex, Kahler, almost Kahler, contact and almost contact, and in the relativity theory was established later. Using the methods of differential geometry and the theory of homogeneous spaces the problem of investigation of four-dimensional Lie groups with left- invariant metric and harmoniс concircular curvature tensor is reduced to the study of metric Lie algebras with harmoniс concircular curvature tensor. It allows to apply the ideas and methods of the homogeneous spaces theory and symbolic computations, and to obtain complete classification of four-dimensional real Lie algebras of Lie groups with left-invariant Riemannian metrics and harmoniс concircular curvature tensor.