1995 Honda Accord 1995 Honda Accord Consuming Oil

My car is consuming oil at an alarmingly (to me) high rate. I find that I have to add a qt a week. I don't smell the oil burning but there is a thick cloud of white smoke when I crank it up in the mornings. I just drove 500 miles & it burned about 2.5 qts on that road trip. Someone told me to add a qt of Morey's oil stabilizer which I did, and saw no diffenerence.