Let X be a non-hyperelliptic curve of genus g which is a double covering of a hyperelliptic curve C of genus h. In this paper, we prove that, if h >=3 and g>= 4h+5, then X admits a complete, base point free g^{1}_{g−2}. Moreover, if h = 3, this result holds under the mild condition g >= 4h+3 = 15.