This paper aims to first develop a model that analyzes how investors place orders in an order driven market. In this model, investors have different share evaluations and information is asymmetric. Private information is short-lived, and types of orders include a market order and a limit order. A market with or without bid-ask prices can influence investors¡¦ choices when submitting market orders. Hence, we discuss two kinds of market conditions in the first model. The first condition is a market with bid-ask prices, and the second is a market without bid-ask prices. Secondly, we develop an integrated model to analyze how an informed trader optimally chooses any combination of a market buy, market sell, limit buy and limit sell. In this model the informed trader observes the terminal value of a security. Then, the trader makes a choice of orders to submit under a market with bid-ask prices. As for the first model, there are some results in the first condition. At equilibrium, the optimal price of a limit order placed by an uninformed trader is related to the difference in share valuation and to adverse selection. The uninformed trader will request adverse selection risk premium, and the risk premium is related to the proportion of informed traders in the market and the value of private information. At this moment, informed traders get information benefits by submitting market orders. The information benefits are related to the difference in share valuation and the value of private information. On the other hand, we have found that informed traders will also experience adverse selection problem when placing limit orders and request risk premiums in limit prices. Informed traders¡¦ limit orders will be executed with the market orders of informed and uninformed traders who will be submitting next. The adverse selection risk of informed traders¡¦ limit orders is only related to private information value if uninformed traders don¡¦t place market orders. However, when uninformed traders submit only market orders, the adverse selection risk is related to the ratio of informed traders and private information value. From the first model, our results indicate the behaviors of informed traders who cannot submit market orders under a market with private information are short-lived like those of uninformed traders. However, we would like to know if an informed trader may submit a limit order. In the second model, in order to get information profit, the informed trader submits not only a market order, but also a limit order, even if the market has bid-ask prices and private information is not short-lived again. A combination of market-limit orders is more profitable than only a market order. In addition, limit orders enhance the profitability of market orders by reducing their losses in bad states. Finally, we obtain the result of price improvement for market orders.