Proposed is an improvement in the VAD process for the preparation of a porous silica glass preform for double-core optical fibers by using three oxyhydrogen flame burners installed one above the other in a flame hydrolysis chamber in which a porous silica glass body consisting of the center core portion formed by the lowermost burner, side core portion formed by the middle burner and the cladding layer formed by the uppermost burner is gradually pulled up as it grows under rotation. Different from conventional procedures in which the extension of the nozzle axis of each of the burners intersects with the rotation axis of the growing body, the extension of the nozzle axis of the middle burner for the side core is displaced in a horizontal direction by a limited distance not to intersect nor to be in parallel with the rotation axis in the invention. By this means, an improvement is obtained in the uniformity of distribution of the refractive index in the side core which otherwise is remarkably disordered.