Statistics from the General Teaching Council for Scotland (GTCS) show there was a total of 113 teachers in that category in 2011-12.
In 2012-13, there were 158 fresh cases where teachers were allowed to remain registered after the GTCS was informed of criminal convictions - up 39.8% on the previous year.
The regulatory body said decisions are made upon a person's fitness to teach and it pointed to the fact that there are more than 70,000 registered teachers in Scotland.
Most of the cases related to road traffic offences. A number of others were for breaches of the peace for which the individual was either fined or admonished.
In 2011-12, one teacher was allowed to stay on the register after being convicted of an "offence relating to committing a sexual act in public".
Another conviction that year was for shoplifting while a third was for "wrongful communication of secret information" dating back to the 1960s.
In 2012-13, offences included an assault where the individual was fined and another where they were given a community service order.
The figures were released by the GTCS following a freedom of information request lodged by the Scottish Daily Mail.
A GTCS spokeswoman said: "There are around 71,000 teachers on the GTCS register of teachers.
"As a firm and fair regulator we investigate thoroughly all of the circumstances surrounding a case and make a decision based upon a teacher's fitness to teach.
"It is important to remember that registration is based on an individual's fitness to teach.
"For example, there are certain offences that bear no relation to the suitability or otherwise of an individual to teach in a school in Scotland.
"We are a firm but fair regulator and we work hard in the public interest and with our partners to ensure our children and young people receive the best quality teaching experience."