Police have received reports of incidents over the past several months.
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In each case, the suspect has been described as a white male in his 30s, with short brown hair and a goatee.
On Thursday, authorities released photos of the suspect's vehicle.
The vehicle is a 2015 or newer Nissan Versa with a sunroof and a spoiler on the trunk.
The license plate number is not visible in the photos.
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Madera Unified School District says the suspect has approached students walking home from class.
In one case, investigators say the suspect got out of his car and approached a student, but the student ran away.
Police are increasing patrols in the reported areas during after-school hours.
Anyone who recognizes the vehicle or has information is urged to contact Madera Police at 559-675-4200.
Callers can remain anonymous.