More action is also need to protect youngsters on social media sites like Facebook and Twitter from bullying, according to the Independent Advisory Group on Hate Crime.
It warns that "prejudice and fear remains a part of everyday life" for many Scots in a report today.
The current law does include aggravations in prejudice-based crimes covering race, religion, sexual orientation and disability.
But today's report warns that there is no similar protections on the basis of gender or age for those seeking refuge from global troublespots in Scotland.
"Questions were raised regarding the extent to which laws protect groups such as asylum seekers and refugees, and this is something that requires further reflection," the taskforce report goes
"We therefore recommend that the Scottish Government should consider whether the existing criminal law provides sufficient protections for those who may be at risk of hate crime, for example based on gender, age or membership or other groups such as refugees and asylum seekers."
Scotland recently accepted its 1000th refugee from Syria as part of efforts to ease the international crisis in the country.
Online abuse is described as a "rapidly growing phenomenon" which is being used to target vulnerable people and perpetrate bullying. "This is increasingly an issue for children and young people, who are more likely to use such technology and therefore be negatively impacted when being subject to bullying or hate crime through social media platforms," it adds.
"Alongside justice agencies, providers of social media such as Facebook and Twitter have an important role in tackling online abuse."
Duncan Morrow, Chair of the Independent Advisory Group: “We found that hate crime remains an all too real issue with real effects on individuals, families, communities and social cohesion. Attacks spread fear to all those who know that they too could face the same violence, and isolates the victims from the rest of society. This in turn fuels prejudice.
“We know that this issue is taken very seriously in Scotland but we heard from too many that reported hate crime is only part of the story."
The Scottish Government's Equalities Secretary Angela Constance said ministers would consider the report's recommendations in full.
“The Scottish Government is committed to doing all that we can to prevent and eradicate hate crime and prejudice, and build community cohesion," she added.
“Let me be clear - there is absolutely no place for bigotry and prejudice in Scotland."