With the increasing requirements of the performance in secure communication filed based on chaos, chaotic systems have been gradually developed into higher dimensions. Because the sequence generated by onedimension chaos, such as Chebyshev map has the problem of weak chaotic properties and uneven distribution, a new two-dimensional chaotic map, called Logistic-Adjusted-Chebyshev map (2D-LACM), is proposed in this paper which enlarges the range of chaotic control parameter, and expands the range of surjection to the entire control parameter interval to make the distribution of the sequence more uniform. Compared with other improved chaotic maps, the proposed 2D-LACM in this paper has more complex chaotic properties and better ergodicity. Next, a visualized image encryption algorithm based on 2D-LACM is proposed (LACM-VIEA), which can encrypt the plain image into a noisy image, and then embed it into a cover image of the same size. In order to demonstrate the security of LACM-VIEA, the algorithm is analyzed in detail from the aspects of key, histogram, visual effect, robustness and anti-plaintext attacks, etc. The final analysis results show that LACM-VIEA has good security performance.