Chaotic maps that can provide highly secure key sequences and ease of structure implementation are predominant requirements in image encryption systems. One Dimensional (1D) chaotic maps have the advantage of a simple structure and can be easily implemented by software and hardware. However, key sequences produced by 1D chaotic maps are not adequately secure. Therefore, to improve the 1D chaotic maps sequence security, we propose two chaotic maps: 1D Improved Logistic Map (1D-ILM) and 1D Improved Quadratic Map (1D-IQM). The proposed maps have shown higher efficiency than existing maps in terms of Lyapunov exponent, complexity, wider chaotic range, and higher sensitivity. Additionally, we present an efficient and fast encryption method based on 1D-ILM and 1D-IQM to enhance image encryption system performance. This paper also introduces a key expansion method to reduce the number of chaotic map iteration needs, thereby decreasing encryption time. The security analyses and experimental results are confirmed that 2D Correlation Coefficient (CC) Information Entropy (IE), Number of Pixels Change Rate (NPCR), Unified Average Changing Intensity (UACI), Mean Absolute Error (MAE), and decryption quality are able to meet the encryption security demands (CC = −0.00139, IE = 7.9990, NPCR = 99.6114%, UACI = 33.46952% and MAE = 85.3473). Furthermore, the proposed keyspace reaches 10240, and the encryption time is 0.025s for an image with a size of 256 × 256. The proposed system can yield efficacious security results compared to obtained results from other encryption systems.