Lucy Letby, 33, was sentenced last year to life in prison with no chance of release.
A jury at Manchester Crown Court had found her guilty of the seven murders between June 2015 and June 2016 at the neonatal unit at the Countess of Chester Hospital in northwestern England.
She was also found guilty of seven murder attempts involving six other babies there but was cleared of two additional charges of attempted murder.
The jury was unable to reach a verdict on several other charges.
The 34-year-old lodged an application for permission to appeal against her convictions in September.
A judicial spokesperson told the BBC that a judge in the Court of Appeal has refused the application after considering the case.
Typically, applications for permission to appeal against a crown court decision are considered by a judge without a hearing. If the bid is refused, the guilty parties have the right to renew their bid at a full court hearing before two or three judges.
Letby’s motives remain unclear, but the scale of her crimes pointed to intricate planning.
