Multiband RF filters with independently controllable passbands are an essential component in dynamic multiband RF communications. Unfortunately, even a fixed multiband RF filter without the capability to adjust the passband properties individually is very difficult to achieve using either RF electronics or microwave photonic technologies. In microwave photonic approaches, the critical limitation is the close relationship between passbands-the tuning of one passband leads to a change in another, hindering the ability to independently control each passband. In this Letter, a programmable microwave photonic multiband filter with full control of amplitude, frequency, bandwidth, group delay slope, and the spectral shape of each passband has been experimentally demonstrated. A multiband filter design algorithm has also been developed that considers each RF passband as an individual, then uses inverse Fourier transform and filter design rule to determine the corresponding optical parameters and combines a series of shaped cosine functions to achieve the desired RF properties.