I fit my dataset to the random forest classifier and found that the model performance would vary among different sets of train and test data split. As what I have observed, it would jump from 0.67 to 0.75 in AUC under ROC curve (fitted by the same model under same setting of parameters) and the underlying range may be wider than that. So what is the issue behind this phenomena and how to deal with this problem? As my understanding, cross validation is used for a specific split of train and test data. 
The model performance vary between different train-test split?
machine learning;random forest;training
While training, your model will not have the same output when you train with different parts of the dataset.  Cross validation is used to help negate this, by rotating the training and validation sets and training more.Your dataset most likely has high variance, given the large jump in accuracy based on different validation sets.  This means that the data is spread out, and can result in overfitting the model.  You can imagine an overfitted model like this:The green line represents the overfitted model.Common techniques to reduce overfitting in random forests is k-fold Cross Validation, with k being between 5 and 10, and growing a larger forest.