Prediction cost of construction project requires large information and data about the project. This makes the prediction cost very complex at the early stage because of limitation of data and information at this stage. The aim of the study is building prediction model to predict cost of construction project in Iraq. To develop the prediction model, Multiple Linear Regression technique (MLR) with Weighted Least Square (WLS) was used. The researcher use 501 set of historical cost data gathered in Iraq for period (2005-2015) for developing the model. The cost of twenty five items of project are used for cost forecasting by MLR model and they involved cost of (excavation the foundation works, Landfill works, filling with sub-base works, Construction works under moisture proof layer, Construction works above moisture proof layer, Construction works of sections, ordinary concrete for walkways, reinforced concrete foundation, reinforced concrete column, reinforced concrete lintel, reinforced concrete slabs, reinforced concrete beams, reinforced concrete stair, reinforced concrete for the sun bumper, plaster finishing works, cement finishing works, Plastic Paints, Pentellite paints, Stone packaging, Works of placing marble, Ceramic works for floor, Ceramic works for walls, Flattening (two opposite layers of lime), Flattening (Tiling). The result shows that MLR with WLS has the capability to predict construction cost with a height coefficient of correlation 95.8%, degree of accuracy 98.97% and smallest mean absolute percentage error 1.03%. MLR with WLS have shown to be a promising method for using in the initial stage of construction projects when only limited data and incomplete information set is preparing for cost analysis.