Conditional odds ratio is usually used to quantify the strength of the association between a given disease and a suspected exposure risk factor in matched-pair design. It has important clinical significance in medical research. In this paper four methods used to construct the asympotic confidence interval of conditional odds ratio under trinomial sampling, Delta method, log transformation method, an improved method based on Filler's theorem and score statistics method respectively. Each method has its own advantages and disadvantages. It is an innovation of this paper to consider the confidence interval of the conditional odds ratio under the trinomial sampling. We use Monte Carlo simulation to evaluate the four interval estimation methods based on the coverage of interval to conditional odds ratio and the average interval length. Finally, two empirical cases are used to show the different characteristics of four interval estimation methods.