Classification affected by a lot of outliers in features? How do you deal with outliers?
If the number of outliers is small and you are concerned that they will destabilize your solution, you could attempt a random forest classifier. The RF fits trees to random selections of data and variables, and collects "votes" from each, thus reducing the impact of outlier valuers.

On the other hand, if the number of outliers is fairly substantital, you might want to create a new class called "outlier". In the training set, apply this label to those values you have deemed to be outliers and then fit the model with the augmented class. Check if the model correctly identifies outliers in the test set. 

This is equivalent to removing the outliers, only it creates a repeatable and machine learning way of doing so.