Is there a length-preserving encryption scheme, that preserves the lengths of input sizes such that the length of the input plain text is same as length of the output cipher text ?
Your are looking for a encryption scheme that supports length preserving encryption. I recommend to use an authenticated encryption scheme like OCB or McOE. There are two common techniques to achieve this goal:
Note that you need at least either a nonce or authentication tag -- or better both -- to preserve data privacy, i.e., security against chosen plaintext attacks (CPA).
Maybe I got you wrong. Maybe you are looking for format-preserving encryption or something else. Hence, a more detailed problem description would be great.
One could design length (and format) preserving encryption schemes using Luby Rackoff Constructions (which are based on Feistel Networks)
While there are variety of variants to achieve (especially , the FFX modes of encryption ) one more notable work is done by Naor and Reigold . They introduce another layer to classic Feistel networks by using Pair-wise Independent Functions ( PWIP), which they prove to be more secure than classic version.
We have very recently re-designed their work and proposed a new, FNR mode of encryption  which is practical arbitrary length block cipher algorithm to do the same . One could build format-preserving-encryption using such scheme. Which is variant of Naor and Reingold's work .
 Naor, Moni, and Omer Reingold. "On the Construction of Pseudorandom Permutations: Luby—Rackoff Revisited." Journal of Cryptology 12.1 (1999): 29-66.