This paper provides tests of the random walk hypothesis for the Korean stock market over the period from March 1988 to December 1998. During this time there are five regimes of daily price limits. We use a sample of 55 actively traded stocks selected to cover a wide range of industries and with a marked number of limit moves and test the random walk hypothesis under each price limit regime. The system of price limits prevents equity prices from following a random walk process and so results in the market being inefficient. As the daily price limits are increased, the proportion of stock prices following a random walk increases. That is, the stock market as a whole approaches a random walk as price limits are relaxed.