The formation of laser-induced periodic surface structures (LIPSS) is demonstrated on a titanium surface irradiated by a double-pulse beam cross-polarized at time delays from Delta tau = 0-1 ps. The first-pulse fluence F-1 and the delayed pulse fluence F-2 are kept below the formation threshold F-TH = 65 mJ/cm(2) of the periodic grating structure on Ti. We find that periodic grating structures with LIPSS orientation of 45 degrees relative to both polarizations are produced at delay times of 0 and 120 fs. To control LIPSS orientation, a double-pulse beam with a time delay of 0 fs is demonstrated in which a beam composed of a first pulse maintaining constant fluence of F-1 = 70 mJ/cm(2) and a delayed pulse varying from F-2 = 0-70 mJ/cm(2). The LIPSS orientations are in a range of 0 degrees-45 degrees and decrease as the normalized fluence F-2/F-1 decreases. We find that the orientation of LIPSS produced by double-pulse irradiations is in relatively good agreement with the direction obtained by the vector sum of laser fields E-1(4) and E-2(4). This tendency suggests that a multi-photon process at the metal surface might characterize the LIPSS orientation.