In this study, a new method is presented for the fundamental frequency estimation of Turkish maqam music recordings by using Variational Mode Decomposition. Variational Mode Decomposition is a method to decompose a real-valued signal into an ensemble of sub-signals (modes) which is entirely non-recursive, determines the relevant bands adaptively and estimates the corresponding modes concurrently. In order to decompose a given signal optimally, Variational Mode Decomposition obtains an ensemble of modes with narrow-band properties similar to the Intrinsic Mode Function definition used in Empirical Mode Decomposition. In this study, we propose using the ElasticNet Regression instead of the Tikhonow Regularization during the optimization stage of the classical Variational Mode Decomposition algorithm to improve the fundamental frequency estimation performance. Frequency estimation algorithm is applied on the autocorrelation function of the music signal to further improve the results. Simulation results on real music and synthetic test data show better or comparable performance to other common decomposition methods for music signals such as spectrogram, YIN, MELODIA and original Variational Mode Decomposition methods.