Travel huge distance in a short time I know that according to the thought experiment by einstein, one who would travel at speed close to light's speed would not age and those on earth would age.
But is it possible for someone to travel from earth to a distant star and come back to earth and yet very small time has passed on earth?
 A: No. Or at least not in special relativity - general relativity complicates matters a bit.
The maths behind this conclusion is discussed in this answer to What is time dilation really? The explanation there is possibly more detailed than you wanted, but I don't think there is a simpler way to explain this. Without the maths all we can say is that the elapsed time for a trip between the same two start points is always greatest for an unaccelerated observer. Since the astronaut going to the distant star has to decelerate at the star then accelerate back to reach Earth again we know that the elapsed time on the spaceship must be smaller than the elapsed time on Earth.
General relativity does make it possible, though not in a very exciting way. For observers on the surface of the earth time runs slowly due to the gravitational time dilation by a factor of:
$$ \frac{t_\text{Earth}}{t_\text{space}} = \sqrt{1 - \frac{2GM}{c^2r_\text{Earth}}} $$
where $M$ is the mass of the Earth and $r_\text{Earth}$ is the radius of the Earth.
So if you left Earth and hovered a few million miles away for long enough eventually your clock would show a greater elapsed time that the clocks on Earth.
