A novel approach for the implementation of microwave photonic filter with positive and negative coefficients based on an unbalanced Mach-Zehnder modulator (MZM) is proposed. In the proposed filter, a microwave signal to be filtered is applied to an unbalanced MZM. Thanks to the unbalance between the two arms of the modulator, a π phase shift is obtained by adjusting the wavelength interval between the adjacent wavelengths, which leads to the generation of the positive and negative coefficients. The theoretical fundamentals of the design are described, which show that the required unbalanced MZM in the scheme can be well fabricated by the current technology, and the required other components, including the wavelength multiplexer, are also commercially available devices. An eight-tap microwave photonic filter with positive and negative coefficients is demonstrated. The tunability and reconfigurability of the eight-tap microwave photonic filter are also investigated to verify our approach.