The victim was targeted after getting off a Leeds-bound Yorkshire Coastliner bus in York Road near to the junction with Stanks Lane North, Swarcliffe.
It was then that the suspect, who had been on the same bus, approached her and asked for directions.
He grabbed hold of her and demanded her phone, but the victim refused and managed to run off.
The man then pursued her but was chased away by the girl's mother who was waiting nearby to meet her.
PC Alana Scott, of Leeds District Crime Team, said: "The images of the suspect are very clear and we hope someone will be able to tell us who it is.
"This was understandably a very distressing incident for the victim and we would urge anyone who recognises him to contact us immediately."
The incident happened at about 4.05pm on Friday, March 17.
The man, who had boarded the bus in Blossom Street, York, is shown on CCTV images waiting to get off in York Road.
Anyone with information is asked to contact PC 2129 Scott at Elland Road via 101, quoting crime number 13170123229.
Alternatively information can be passed on to the independent crime Crimestoppers anonymously on 0800 555 111.