The chromatin landscape regulates transcription by localizing and regulating the activity of sequence-specific DNA binding proteins, chromatin remodeling enzymes and transcription machinery. Pioneer transcription factors can target DNA motifs on closed chromatin and trigger local chromatin remodeling to increase chromatin accessibility. Despite this knowledge, how pioneer factors search for their cognate motif on chromatin remains poorly understood. Here, we use multicolor single-molecule fluorescence resonance energy transfer (smFRET) to investigate how a prototypical Drosophila pioneer factor GAF locates its cognate motif on chromatin. To investigate how GAF searches for its cognate motif on DNA and nucleosomes, we strategically placed fluorophores on the DNA binding domain of GAF (GAF-DBD) and DNA motifs, allowing distinction of motif-specific binding and nonspecific DNA binding by FRET. We observed GAF-DBD dwells on a DNA molecule containing one GAF binding motif for 3-4 seconds before dissociation. Interestingly, on a DNA sequence with two GAF binding motifs, GAF-DBD can slide between two motifs while staying bound to the DNA. This suggests GAF monomers use one-dimensional (1D) sliding to search for its motif on nucleosome-free DNA. We next investigated the scenario where one of the two motifs is protected by a nucleosome. If the motif is located at the edge of a 601 nucleosome (SHL7 location), GAF-DBD more frequently lands on the other motif on linker DNA before it slides to the nucleosomal motif. Nucleosomes effectively block 1D sliding when the motif is located more internally on the nucleosome, at SHL5 or SHL3. However, on a nucleosome reconstituted on a native Drosophila DNA sequence, GAF-DBD can directly target internal motifs by three-dimensional diffusion, instead of 1D sliding. Our findings reveal different search modes that can be used by pioneer factors to locate their cognate motifs on chromatin.