Decoder-side intra mode derivation (DIMD) is a promising coding tool in the enhanced compression model (ECM) developed by the joint video experts team (JVET). In DIMD, the intra prediction mode of a luma block is derived based on the gradient information of the adjacent luma samples at both encoder and decoder, rather than being explicitly signaled in the bitstream. Inspired by DIMD, a decoder-side chroma intra mode derivation (DCIMD) method is proposed in this paper to improve the coding efficiency of chroma intra prediction. In the proposed DCIMD, the gradient information of both adjacent luma samples and chroma samples is utilized to derive an angular intra mode to predict the current chroma block. There are two advantages to this proposed scheme: 1). the combination of luma information and chroma information can ensure that the derived angular intra mode is closely matched with the texture features of the current chroma block; 2). the number of chroma intra prediction modes can be effectively extended by introducing DCIMD as a new mode without incurring additional expensive bit overhead. Moreover, to further improve the coding efficiency of DCIMD, a chroma intra mode fusion (CIMF) method is proposed. In CIMF, predictions from the DCIMD chroma prediction mode and a cross-component correlation-based chroma prediction mode can be fused together with adaptive weights. Simulation results show that on top of ECM-4.0 the BD-rate savings of 0.07%, 1.17%, and 1.02% on average for Y, Cb, and Cr components, respectively, are achieved in all intra configuration with the proposed two methods. Both the proposed DCIMD and CIMF methods have been adopted into the ECM-5.0 by JVET.