diff --git a/DynamicProgramming/LongestPalindromicSubstring.java b/DynamicProgramming/LongestPalindromicSubstring.java
new file mode 100644
index 000000000..5bef01eb1
--- /dev/null
+++ b/DynamicProgramming/LongestPalindromicSubstring.java
@@ -0,0 +1,56 @@
+package test;
+
+import java.io.*;
+import java.util.*;
+
+/*
+ * Algorithm explanation https://leetcode.com/problems/longest-palindromic-substring/
+ */
+public class LongestPalindromicSubstring {
+	public static void main(String[] args) {
+		String a = "babad";
+		String b = "cbbd";
+
+		String aLPS = LPS(a);
+		String bLPS = LPS(b);
+
+		System.out.println(a + " => " + aLPS);
+		System.out.println(b + " => " + bLPS);
+	}
+
+	private static String LPS(String input) {
+		if(input == null || input.length() == 0){
+			return input;
+		}
+		boolean arr[][] = new boolean[input.length()][input.length()];
+		int start = 0, end = 0;
+		for (int g = 0; g < input.length(); g++) {
+			for (int i = 0, j = g; j < input.length(); i++, j++) {
+
+				if (g == 0) {
+					arr[i][j] = true;
+				} else if (g == 1) {
+					if (input.charAt(i) == input.charAt(j)) {
+						arr[i][j] = true;
+					} else {
+						arr[i][j] = false;
+					}
+				} else {
+
+					if (input.charAt(i) == input.charAt(j) && arr[i + 1][j - 1]) {
+						arr[i][j] = true;
+					} else {
+						arr[i][j] = false;
+					}
+				}
+
+				if (arr[i][j]) {
+					start = i;
+					end = j;
+				}
+			}
+		}
+		return input.substring(start, end + 1);
+	}
+
+}