A mixed signal with several unknown modes is common in the industry and is hard to decompose. Variational Mode Decomposition (VMD) was proposed to decompose a signal into several amplitude-modulated modes in 2014, which overcame the limitations of Empirical Mode Decomposition (EMD), such as sensitivity to noise and sampling. We propose an improved VMD, which is simplified as iVMD. In the new algorithm, we further study and improve the mathematical model of VMD to adapt to the decomposition of the broad-band modes. In the new model, the ideal flattest response is applied, which is derived from the mathematical integral form and obtained from different-order derivatives of the improved modes’ definitions. The harmonics can be treated via synthesis in our new model. The iVMD algorithm can decompose the complex harmonic signal and the broad-band modes. The new model is optimized with the alternate direction method of multipliers, and the modes with adaptive broad-band and their respective center frequencies can be decomposed. the experimental results show that iVMD is an effective algorithm based on the artificial and real data collected in our experiments.