In a report entitled 'Second-Rate Justice', Liberty says a number of cases were brought to its attention which it says revealed "serious and fundamental problems in the way in which service personnel or their bereaved families were being treated by the Armed Forces and the Ministry of Defence".
It is particularly critical of the way in which cases involving rape or other serious offences are handled.
Liberty say that in 2017, 48 rape cases were taken to trial in court martial, with two resulting in convictions – which the human rights group say is a lower rate of conviction than in civilian courts.
In total, Liberty's report has 21 recommendations for the military, including that all serious criminal offences committed in the United Kingdom are investigated by civilian police.
They also advise that an independent expert supervisory body be established to provide oversight of the Service Police and that the three branches of the service police are combined into a single force.
It also suggests that the independent Service Complaints Ombudsman be involved at an early stage in serious cases of bullying, sexual harassment or racial or other discrimination.
Emma Norton, Liberty’s head of legal casework, said: "The serving men and women that contact Liberty have all been on the sharp end of the Service Justice System.
"They may have been sexually harassed, sexually assaulted, beaten or abused – or they may have tried to raise a complaint but found that it has had a detrimental impact on them or their career.
"It ought to be beyond discussion that the investigation of serious criminal offences such as rape or other serious assaults should be handled by the civilian police, not the Service Police who lack the resources, experience and expertise.
"If the Ministry of Defence is serious about tackling unhealthy attitudes or patterns of behaviour in the forces, what better way to demonstrate that than by ensuring independent police always investigate and have oversight of those difficult cases?"
An MOD spokesperson said: "The service justice system closely mirrors the system for civilians. It is subject to regular parliamentary oversight and police investigations are independent of the military chain of command.
"In order to ensure the system continues to operate effectively, an independent review is currently underway, which Liberty has recently fed into.
"We continue to provide a wide range of support to victims and, if needed, there are various mechanisms through which personnel can raise concerns, including through the Service Complaints system."
The new helpline will be open from 10am-4pm Monday to Friday. It is free to call for service personnel and their families on 020 3102 9313.