We report an experimental observation of wavelength tuning and bound states in fiber lasers. A Mach-Zehnder interferometer (MZI) is adopted as an intra-cavity tunable filter to realize large-scale wavelength tuning and bandwidth controlling. By finely manipulating the MZI and intra-cavity polarization state, continuous wavelength-tunable operation from 1550.7 nm to 1580.8 nm is achieved. Meanwhile, the spectral bandwidth varying from 1.85 nm to 3.41 nm is also controlled by broadening the free spectrum range (FSR) of the MZI. Additionally, with modest polarization adjustment, both tightly and loosely bound states are experimentally observed, which can be validated by the numerical simulations. The results indicate that the proposed fiber laser is attractive for telecommunication systems, on account that the tuning feature can be applied to wavelength-division multiplexer (WDM) and the various soliton bound states could contribute to the high-level modulation format.