Cryptography and steganography is a method to secure private data. Those methods can also be combined for a more robust data security method. In this paper, we proposed a combination of cryptography and steganography methods that exploit some properties of Deoxyribonucleic Acid (DNA) for securing private data. The proposed work aims to enhance a POST-quantum DNA cryptography method by combining it with the steganography method. There are two parts to the proposed method; the first one is to encrypt private messages using a Kyber-DNA cryptography method. The second one is to embed encrypted private messages into a DNA sequence. The proposed method was then compared to another similar method RSA-DNA, El Gamal-DNA, and ECC-DNA. The proposed method is also compared with a similar POST-quantum method, that is NTRU-DNA. All those methods are compared in embedding speed test and extracting speed test. From those tests, it can be concluded that the proposed method has performance slightly lower than El Gamal-DNA and ECC-DNA but faster than RSA-DNA and NTRU-DNA