The problem of time evolution and squeezed states of the generalized quadratic time-dependent harmonic oscillator is studied by making use of the time-evolution operator approach. Then, the squeezed states and high-n squeezed states of the driven harmonic oscillator with strongly pulsating mass are constructed. Finally, we show how the squeezed-coherent states and high-n squeezed-coherent states, which preserve the minimum uncertainty codition, can be generated.