Queensland's attorney-general has failed in a bid to lengthen the jail time of a drug addict who injected a 10-year-old boy with morphine.

The Court of Appeal in Brisbane on Friday rejected the appeal by state Attorney-General Cameron Dick against the sentence given to Denny John Brown, 28, in July.

Brown was jailed for six years with a recommendation for parole after two years after he pleaded guilty in the Supreme Court in Brisbane to a series of offences including unlawful wounding, stealing and impersonating a police officer.

The court heard Brown was living with his girlfriend at a house in Inala in Brisbane's southwest in 2007 when he used a needle to inject her 10-year-old son with morphine on at least three different occasions.

The boy slept for three days after one of the injections.

Lawyers acting on behalf of Mr Dick took the case to the Court of Appeal last month, where they argued the sentence should be increased to seven years, of which Brown should serve five and a half years.

They also submitted Brown's crimes should be declared serious violent offences.

The Court of Appeal ruled the original sentence was not "inadequate" and that it took into account "weighty mitigating factors" such as prospects of rehabilitation and pleas of guilty.