This paper introduces Conformal Interquantile Regression (CIR), a novel conformal regression method designed to rapidly produce the smallest possible prediction intervals with guaranteed coverage. CIR employs black-box machine learning models to directly estimate outcome distributions through interquantile ranges and then converts these estimates into concise prediction intervals, achieving approximate conditional coverage. Base on CIR, we also introduce a variant, Conditional Interquantile Regression with More Comparation (CIR+), which incorporates an additional decision mechanism that evaluates whether to retain or discard a specific interquantile interval based on its length. The additional step in CIR+ results in slightly narrower prediction set widths while maintaining comparable coverage performance. Both of methods solve two main problems found in other distributional conformal prediction methods: they work well with skewed data, which is challenging for methods like Conformalized Quantile Regression, and they are computationally far more efficient than Conformal Histogram Regression by avoiding the histogram construction process. Empirical studies using both synthetic and real-world datasets demonstrate that our methods achieve the best balance between predictive performance and computational efficiency compared to other approaches.