A wood planing machine includes left and right ends mounted on a base via left and right pairs of posts. The ends are respectively formed with through holes to permit extension of left and right screw rods. Left and right thread members are respectively inserted in the through holes and engage the screw rods. A fine adjusting unit includes a mounting wall mounted on the left end, and a rod member having a first rod section mounted rotatably on the mounting wall, and a second rod section extending eccentrically from the first rod section and received fittingly in an engaging hole in the left thread member such that rotation of the first rod section results in vertical fine movement of the left thread member relative to the left screw rod.