A tunable L-band dissipative soliton (DS) fiber laser with nonlinear polarization rotation (NPR) playing the roles of both a saturable absorber (SA) and a tunable filter has been demonstrated experimentally and numerically. By appropriate adjustment of the states of the polarization controllers (PCs) and the pump power, DSs with continuously tunable wavelengths have been observed over the wavelength range from 1583.0 to 1602.4 nm with a 3-dB spectral bandwidth of around 20 nm and from 1581.9 nm to 1602.6 nm with a 3-dB spectral bandwidth of around 4 nm. In addition, we have observed that by increasing the pump power, the 3-dB spectral bandwidth of the DS could be increased without pulse breaking. Numerical results for the characteristics of the DSs are in accord with the experimental data.