In　this　paper,　we　have　introduced　a　new　approach　to　solve　a　class　of　interval　linear　programming　(ILP)　problems.　Firstly,　the　novel　concept　of　an　interval　ordering　relation　is　further　developed　to　make　desired　solution　feasible.　Secondly,　according　to　the　3σ　law　of　normal　distribution,　a　new　equivalent　transformation　for　constraints　with　the　interval-valued　coefficients　of　ILP　is　justified.　Accordingly,　the　uncertainty　stemmed　from　interval　number　could　be　replaced　by　the　uncertainty　of　random　variables.　Consequently,　the　classical　methodology　of　stochastic　linear　programming,　a　chance　constrained　programming　model　based　on　normal　distribution　is　designed　to　work　out　the　equivalent　form　of　the　original　problem.　This　is　because　it　allows　us　to　carry　out　the　optimization　operation　with　a　certain　calibrated　probability.　A　typical　numerical　example　is　given　to　illustrate　how　to　apply　equivalent　transformation　in　order　to　realize　ILP.　Finally,　we　conclude　this　paper　by　elaborated　comparisons　among　our　method　and　selected　existing　solutions　to　advance　our　confidence　of　our　research　results　as　to　their　correctness　and　effectiveness.　©　2015,　Springer　Science+Business　Media　New　York.