This no link between the Debye length and the zeta potential. The Debye length depends on the ionic strength of the solution where you dispersed the particles.

Thank you for your response Sir. But I heard that some formula is there for calculate this value from zeta potential value.

So, it seems from your answer that both are different. am i right?

As Patrice stated - in other words zeta potential can be the same for different systems with different ionic strength, i.e. Debye length can be different.

The relation to Debye length is that you can only apply Smoluchowski approach to calculate the zeta potential if only for a sufficiently thin double layer, when the Debye length, 1/κ, is much smaller than the particle radius a.

See e.g. Wikipedia for zeta potential.