ElGamal as an asymmetric key cryptography system and Data Encryption Standard (DES) as a symmetric key cryptography system, both of algorithms will be compared using the time complexity analysis and computer simulation. The result of time analysis shows a different complexity for both algorithms, there is quadratic complexity for ElGamal Algorithm and Linear Complexity for DES algorithm. Input that is used by ElGamal algorithm is the private key, while for DES algorithm is the plaintext's size. Based on result of simulation using a computer program, it shows a significant timing differences, ElGamal's time execution is longer than DES. This is caused by differences of arithmetic operations that is used by each algorithms.