The　time　dependent　vehicle　routing　problem　(TDVRP)　is　defined　as　a　vehicle　fleet　of　fixed　capacities　serves　customers　of　fixed　demands　from　a　central　depot　with　consideration　of　road　networks　conditions.　The　travel　time　between　two　customers　or　between　customer　and　the　depot　depends　on　the　distance　of　the　two　points　and　time　of　a　day.　A　mathematical　model　is　formulated　for　the　TDVRP　problem　and　a　simulated　annealing　(SA)　based　improvement　method　is　proposed　for　solving　it.　The　main　objective　is　to　minimize　the　number　of　vehicles　and　the　second　objective　is　to　minimize　the　total　travel　distance　of　the　vehicles.　The　proposed　approach　was　tested　on　the　56　test　problems　with　100　customers　from　Figliozzi＇s　benchmark,　and　results　show　that　the　improvement　metaheuristic　could　get　better　solutions　than　Figliozzi＇s　algorithm　in　the　different　time　dependent　speeds　function　within　an　accepted　computational　time.　©　2016　SERSC.