In this paper,we propose an eye gazing estimation method by using single camera and single light source based on twice polynomial fitting to overcome the common drawbacks of gazing estimation system with one camera but no light source,i.e.,low accuracy and restricted head movement.After the corneal reflection spot and the iris center have been precisely located,we study the mapping relationship between the iris center displacement relative to the corneal reflection spot and the gazing point on the test board.We use the first polynomial fitting to address how the relative displacement of iris center change when the location of the reflection point changes while the gazing point is fixed.In this way,we can calculate the ideal iris center displacement relative to any given reflection point position when the testee is gazing at the fifteen test points on the board.Then we use the second polynomial fitting to study the relationship between the relative displacement of iris center and the gazing point when the location of the reflection spot is determined.By using twice polynomial fitting,we achieve a valid estimation of the gazing point on the test board with unrestricted head movement.The horizontal average error of the test samples is 1.31° and the vertical average error is 1.00°.