Robert Bayne, 22, was ordered to serve at least 20 years in prison when he was given a life sentence after being found guilty of murdering Zoe Nelson, 17, last year.
Bayne challenged the minimum period of imprisonment imposed on him by the trial judge, Lady Dorrian, claiming it was excessive.
His counsel, Chris Shead, argued that his crime “however repugnant” could not be regarded in the categories of murder where previous appeal court guidance had established there should be sentences at that level.
Lord Reed, sitting with Lord Brodie, at the Court of Criminal Appeal in Edinburgh, said that sentencing was not a precise science but the trial judge was very experienced and best placed to make the decision.
“The sentence was arguably at the upper end of the range, but that reflects her assessment of the gravity of the case having heard the evidence over a number of weeks,” said Lord Reed, in refusing the appeal.
Bayne was found guilty of murdering Miss Nelson on the edge of Wishaw, Lanarkshire, at the High Court in Edinburgh. He was found guilty of repeatedly striking her in May 2010 on the head and body.