RS232/RS485 Converter Circuit Receiving Problem
in my circuit, 2 pin connector was used as RS485 connector and only
  A,B connecitons were made. (RI and ground connections were not used.)


RS485 proper wiring requires a common earth: -



You cannot expect disparate systems having their own ground connections to adequately handle the common mode noise that is normally present between separate grounds.

In addition the maxim document linked states: -


  Although RS-485 can be successfully transmitted using multiple types
  of media, it should be used with wiring commonly called "twisted
  pair." What Is Twisted Pair, and Why Is It Used?
  
  As its name implies, a twisted pair is simply a pair of wires of equal
  length and twisted together. Using an RS-485-compliant transmitter
  with twisted-pair wire reduces two major sources of problems for
  designers of high-speed long-distance networks: radiated EMI and
  received EMI.


I always use screened twisted pair with matching terminators. 

You have not even attempted to use the 120R (across A and B) terminator.