A man who allegedly drove his car into a group of pedestrians on a Sydney footpath had not slept since consuming methamphetamine three days earlier, a court has heard.

The victims - three women and a two-year-old girl - were seriously injured when they were struck as they walked along Canterbury Road in Belmore on Sunday afternoon.

Newtown Local Court heard the alleged driver, Peter Bosilkovski, has a lengthy criminal history, and was previously convicted of dangerous driving and driving while disqualified.

Magistrate Robbie Williams said: "More recently, there has been a history of violence."

The court heard the 50-year-old was already on bail for two other offences when he was charged with five driving offences, including three counts of dangerous driving occasioning grievous bodily harm.

Prosecutors said Bosilkovski consumed a tenth of a gram of the drug ice three days before the crash, and had not slept since.

He also allegedly tried to disguise the fact he was the driver.

Asked to consider releasing Bosilkovski on bail, Magistrate Williams said: "There is an unacceptable risk, particularly of the commission of further offences and fail to appear.

"On that basis, bail is refused."

The women - aged 49, 23 and 21 - were all taken to hospital with serious injuries after the crash.

The toddler sustained serious head injuries.

The case will return to court next month.

Police have asked witnesses to contact Crime Stoppers.