We derive, with an invariant operator method and unitary transformation approach, that the Schr(o)dinger equation with a time-dependent linear potential possesses an infinite string of shape-preseving wave-packet states |ψα,λ(t)>having classical motion. The qualitative properties of the invariant eigenvalue spectrum (discrete or continuous)are described separately for the different values of the frequency ω of a harmonic oscillator. It is also shown that,for a discrete eigenvalue spectrum, the states |ψα,n(t)> could be obtained from the coherent state |ψα,0(t)>.