This paper presents the effective lossy and lossless color image compression algorithm with Multilayer perceptron. The parallel structure of neural network and the concept of image compression combined to yield a better reconstructed image with constant bit rate and less computation complexity. Original color image component has been divided into 8x8 blocks. The discrete cosine transform (DCT) applied on each block for lossy compression or discrete wavelet transform (DWT) applied for lossless image compression. The output coefficient values have been normalized by using mod function. These normalized vectors have been passed to Multilayer Perceptron (MLP). This proposed method implements the Back propagation neural network (BPNN) which is suitable for compression process with less convergence time. Performance of the proposed compression work is evaluated based on three ways. First one compared the performance of lossy and lossless compression with BPNN. Second one, evaluated based on different sized hidden layers and proved that increased neurons in hidden layer has been preserved the brightness of an image. Third, the evaluation based on three different types of activation function and the result shows that each function has its own merit. Proposed algorithm has been competed with existing JPEG color compression algorithm based on PSNR measurement. Resultant value denotes that the proposed method well performed to produce the better reconstructed image with PSNR value approximately increased by 21.62%.