Nearly simultaneous observations for 28SiO v=0, 1, 2, J =3-2 transitions in 39 late-type stars have been carried out in February 1995 and 1996 with the 14 m radio telescope at Taeduk Radio Astronomy Observatory (TRAO). Observations for 28SiO v=0, 1, 2, J=2-1 lines in the same objects have been also carried out in March 1995 and March-April 1996. The detection rate of 28SiO v=l, J=3-2 line for the 28SiO v=l, J=2-1 sources was 59%. Seventeen new detections in the 28SiO v=l, J=3-2 transition and 4 new detections in the 28SiO v=2, J=3-2 transition have been reported including the intensity ratios within the vibrational ladders and rotational states.