This　paper　is　concerned　with　numerical　computations　of　a　class　of　biological　models　on　unbounded　spatial　domains.　To　overcome　the　unboundedness　of　spatial　domain,　we　first　construct　efficient　local　absorbing　boundary　conditions　(LABCs)　to　reformulate　the　Cauchy　problem　into　an　initial-boundary　value　(IBV)　problem.　After　that,　we　construct　a　linearized　finite　difference　scheme　for　the　reduced　IVB　problem,　and　provide　the　corresponding　error　estimates　and　stability　analysis.　The　delay-dependent　dynamical　properties　on　the　Nicholson＇s　blowflies　equation　and　the　Mackey-Glass　equation　are　numerically　investigated.　Finally,　numerical　examples　are　given　to　demonstrate　the　efficiency　of　our　LABCs　and　theoretical　results　of　the　numerical　scheme.