For the common key space shortage problem found in existing Arnold digital image encryption algorithm, a new digital image encryption algorithm-SMA (Sparse Matrix Arnold) based on sparse matrix and Arnold transformation was proposed and in order to further improve the security of the algorithm, an improved algorithm-3SMA (3 round SMA) using the ideas of multi-layered decomposition and three-tier structure encryption was proposed. The SMA algorithm adopted Arnold transform to spread the plaintext picture into a large sparse matrix, and then removed invalid sparse matrix elements to get the cipher text. While, the decryption of SMA needed to enter the cipher text picture, and moved pixels in cipher text picture back to their original positions in accordance with the previously computed swapping table. The 3SMA algorithm comprised three different round keys. Each round, the improved algorithm needed to process two color components of the plaintext picture to achieve the purpose of encryption. The experimental results show that the proposed encryption algorithm and its improvement obtain higher security compared to Arnold encryption algorithms analyzed.