We propose the Mood Board Composer (MBC), which supports concept designers in retrieving and composing images on a 2-D concept space to communicate design concepts. The MBC allows users to iterate adaptive image retrievals intuitively. Our new contribution to the mood board tool is to adapt the query vector for the next iteration according to the user's rearrangement of images on the 2-D space. The algorithm emphasizes the meaning of the labels on the x- and y-axes by calculating the mean vector of the images on the mood board multiplied by the weights assigned to each cell of the 3 x 3 grid. The next image search is performed by obtaining the most similar words from the mean vector thus obtained and using them as a new query. In addition to the algorithm described above, we conducted the participant experiment with two other interaction algorithms to compare. The first allows users to delete unwanted images and go on to the next searches. The second utilizes the semantic labels on each image, on which users can provide negative feedback for query modification for the next searches. Although we did not observe significant differences among the three proposed algorithms, our experiment with 420 cases of mood board creation confirmed the effectiveness of adaptive iterations by the Creativity Support Index (CSI) score.