Presented is a more general form of Markov chain random walk with absorbing barriers has the transition probabilities 00 jjp   , 11 L j L jp    , 1L p   , 1 Lp   , 1ii i pq   ,
ii i pr  , 1ii i pp   , 1 1 1 1 p r q
     , 1 L L L p r q
     , 0 , 1   , and
1i i i p r q    for   2,..., 1 iL . Theoretical formulae are given for the mean number of step before absorption, the mean time to absorption as well as the absorption probabilities, when the states placed on a ring network and on one dimensional lattice segment. The results are generalizing previous works. Explicit expressions are also given for certain models, and two simple mathematical models in biology are discussed.