This paper introduces a simple and effective improved one-dimension (1D) Logistic chaotic map. Simulations and performance evaluations show that the improved 1D Logistic chaotic map is able to get larger chaotic range and better chaotic behaviors compared with its prototype map. To investigate its applications in multimedia security, I propose an efficient encryption algorithm for color image. Firstly, used an improved 1D Logistic chaotic map to confuse the addresses of a color image pixels. Secondly, decomposed the resultant image into 24-bits planes to get a bit-matrix containing a mixture of the red, green and blue elements. Finally, utilized global diffusion to permute the bit-matrix which makes the three elements influence each other effectively without neglecting the relativity between R, G and B. Computer simulations indicate that the proposed algorithm has some good properties such as easy to implement, large key space, and excellent encryption effect with just one round of iteration. Hence, it has application in secure communication to enhance the security of transmitting color image.