Based on the model of random walk on the simple cubic lattice

the distribution function of conformation of a polymer chain in an interfacial layer was deduced．If the model chain was consisted of N segments

it was possible to form both the tail chain

when the terminal segments were adsorbed at the interface

and the adsorbed chain with the non-terminal group．The conformational number Ωtail of a tail chain is equal to Ωfree/(6πN)1/2

where Ωfree is the conformational number of a chain in free state and equals to 6N for this random walk model．It was found from theoretical analysis that

for the set of a chain attached non-terminally to the interface

the total conformational number Ωtot is equal to Ωfree/6．As an result

the average conformational number Ωm for the chain attached non-terminally to the interface is Ωfree／6N．In the case of short chain

for instance N is equal to about 10

the conformational number Ωtail of tail chain is even larger than the total number Ωtot. In the limitation of long chain

however

the conformational number Ωtail for tail chain is nuch large than Ωm

but smaller than Ωtot．The conclusion is that the distribution function of conformation for chains in the interfacial layer is not uniform

but has a special distribution form described in this paper．