A tour cover of an edge-weighted graph is a set of edges which forms a closed walk and covers every other edge in the graph. The minimum tour cover problem is to find a minimum weight tour cover.This problem is introduced by Arkin, Halldórsson and Hassin (Information Processing Letters 47:275-282, 1993) where the author prove the NP-hardness of the problem and give a combinatorial 5.5-approximation algorithm. Later Könemann, Konjevod, Parekh, and Sinha [7] improve the approximation factor to 3 by using a linear program of exponential size. The solution of this program involves the ellipsoid method with a separation oracle. In this paper, we present a new approximation algorithm achieving a slightly weaker approximation factor of 3.5 but only dealing with a compact linear program.