  We investigate filling dependence of the zigzag Hubbard ladder, using density
matrix renormalization group method. We illustrate the chemical-potential vs.
electron-density and spin gap vs. electron density curves, which reflect
characteristic properties of the electron state.On the basis of the obtained
phase diagram, we discuss the connection to a novel quasi-one-dimensional
superconductor Pr$_2$Ba$_4$Cu$_7$O$_{15-\delta}$.
