Abstract: By applying discharging method, we showed that a planar graph G with maximum degree four and girth g is of class 1, if it satisfies one of the following conditions. (1) G does not contain cycles of length from 4 to 9; (2) G does not contain 4-cycles and 5-cycles, and two 3-faces are not incident with a common vertex; (3) G does not contain cycles of length from 5 to 8, and two 3-cycles, two 4-cycles are not incident with a common vertex ; (4) g≧geqslant 4, G does not contain chordal-8-cycle, and two 4-faces are not incident with a common vertex.