A strainer filtering apparatus including a filtering tube providing a substantially larger effective filtering area for its length and width, substantially reducing foreign substances covering a suction surface and flow resistance of the foreign substances, and reducing pressure drop at a cooling water passage. The strainer filtering apparatus includes at least one inlet side into which cooling water is introduced and an outlet side through which the cooling water is discharged, hollow filtering tubes with filtering holes along their lengths, an upper plate having first grooves located at a lower surface and coupled to upper ends of the filtering tubes and an inlet part into which the cooling water is introduced, and a lower plate having punched holes to which lower ends of the filtering tubes are coupled. The cooling water in the filtering tubes is introduced through the punched holes and discharged at the outlet side.