The crossed cube, a variation of the hypercube, possesses a better topological property than the hypercube in its diameter that is about half of that of the hypercube. It has been known that an N-node complete binary tree is a subgraph of an (N+1)-node crossed cube [P. Kulasinghe and S. Bettayeb, 1995]. However, efficient embedding methods have not been known for the case that the number of nodes of the complete binary tree is greater than that of the crossed cube. In this paper, we show that an N-node complete binary tree can be embedded into an M-node crossed cube with dilation 1 and load factor [N/M], N>M$geq$2. The dilation and load factor is optimal. Our embedding has a property that the tree nodes on the same level are evenly distributed over the crossed cube nodes. The property is especially useful when tree-structured algorithms are processed on a crossed cube in a level-by-level way.