The party submitted Freedom of Information (FOI) requests to local councils and received responses from three-quarters of them.
The findings, for 2011 and 2012, showed 730 racist incidents reported in primary schools and 544 in secondaries.
The Scottish government said racism in schools would not be tolerated.
There were a total of 1,274 racist incidents reported at schools in 2011 and 2012.
Of these, 667 were recorded in 2011, with the number falling to 607 in 2012.
The figures showed Edinburgh City Council recorded 279 racist incidents in primary schools over the two years, with a further 114 incidents in secondary schools in the capital.
Scotland's largest council, Glasgow City Council, was among the local authorities which did not provide the information requested.
Scottish Lib Dem education spokesman Liam McArthur said the statistics showed Scotland still had "a long way to go" in tackling racism.
He called on ministers to look again at how youngsters were taught about racism and prejudice.
He added: "We all want to see a fairer society where everyone has the chance to get on in life regardless of their racial or ethnic background.
"Over the past five years we have made real progress in tackling racism but the fact that progress seems to have stalled is a concern.
"I do not doubt the commitment of ministers and teachers to battling racism, but these new figures show that we have a long way to go."
He said the figures should act as a "reality check " and addressing these issues should start with education.
"There is a real case for looking again at how we talk to children and young people about racism and teach them that prejudice - in whatever form - is simply not acceptable," Mr McArthur said.
A Scottish government spokeswoman said: "Racist behaviour or bullying is not acceptable and will not be tolerated in any Scottish schools.
"We expect councils and schools to tackle racist behaviour where it does occur.
"Under Curriculum for Excellence pupils will learn about different cultures and beliefs and materials to support teachers in this area are available from Education Scotland."
There have been almost 1,300 racist incidents in Scottish schools in the past two years, according to figures obtained by the Liberal Democrats.