A new method for computing complex bidimensional empirical mode decomposition (BEMD) is presented in this paper. The proposed complex-BEMD uses four quadrant spectra to apply standard BEMD to four real-valued 2D signals. The so-generated intrinsic mode functions (IMFs) are 2D complex-valued, which facilitates the extension of the standard BEMD to the complex domain. The proposed complex-BEMD can be successful for the analysis of real-world 2D complex-valued signals, such as 2D NMR signals. Moreover, the proposed complex-BEMD can be applied for color image processing. A simple color image fusion algorithm based upon the proposed complex-BEMD has also been developed to have the exhibition of the potential. By our proposed complex-BEMD and image fusion algorithm, the well-fused results can be obtained, if the mode mixing in BEMD is alleviated.