Here is a code that sorts string array with Insertion Sort.

public class SortStringArrayUsingInsertionSort{

public static void main(String[] args){
        String[] arr ={"Atlanta","New York","Dallas","Omaha","San Francisco"};
        int count = 0;
        String sortedArray[] = sort_sub(arr, arr.length); 
        for(int i=0;i<sortedArray.length;i++){
            System.out.println(sortedArray[i]);
          }
        }

    public static String[] sort_sub(String array[], int f){
        String temp="";
        for(int i=0;i<f;i++){
            for(int j=i+1;j<f;j++){
               if(array[i].compareToIgnoreCase(array[j])>0){
                   temp = array[i];
                   array[i]=array[j];
                   array[j]=temp;
               }
            }
        }
        return array;
    }
}