At the same time, there was a fall in unemployment, according to the Office for National Statistics, with the total number of people out of work and claiming Jobseeker's Allowance at its lowest level for almost six years.
Employment in Scotland grew by 9,000 over the period April to June, leaving the total 63,000 higher than the same quarter in 2013.
Unemployment dropped by 2,000 over the quarter and 21,000 over the year to stand at 176,000 - with this including some people who are out of work and not eligible for benefits.
A total of 92,900 jobless people were in receipt of Jobseeker's Allowance in July, a drop of 3,100 on the previous month and 35,500 lower than in July 2013.
The unemployment rate in Scotland is now the same as that for the UK as a whole, at 6.4%.
But the employment rate north of the border is 73.5%, which is higher than the UK rate of 73%.
Scottish Secretary Alistair Carmichael said: "Today's figures show we have a new record high in overall employment. Over the last 12 months Scottish employment has increased by 63,000 and unemployment has fallen by 21,000.
"This shows that working together as part of the UK with its larger market, stronger and growing economy and stable currency is creating more jobs and better opportunities for Scotland.
"It is also good to see the number of people claiming Jobseeker's Allowance continues to fall. It is now at its lowest level since October 2008 and is 35,500 lower than one year ago.
"Each one of the figures today represents another person or household getting back into the labour market. It also represents the certainty, stability and security we are creating for businesses by being part of the UK.
"We will continue with our long term economic plan to ensure that these positive figures are reflected in communities across the length and breadth of Scotland and our businesses have the confidence to grow and employ more Scots."
Angela Constance, the Training, Youth and Women's Employment Secretary in the Scottish Government, said the statistics show economic recovery "is continuing to gain momentum, with unemployment down and employment at its highest level ever".
She said both youth employment and female employment had increased over the period April to June, with the number of women in work reaching a record high of 1,250,000 - a rise of 36,000 over the year.
"Female employment continues to increase and now sits at the highest level since records began, and the female unemployment rate is at its lowest since May-July 2009," Ms Constance said.
"This Government will always do everything we can to ensure women have the same opportunities in the labour market as their male counterparts, and have access to quality sustained work in careers they choose.
"As part of our recovery we must ensure that everyone is able to benefit from a growing economy. For example, our transformational plans for childcare will not just be good for children, but also their parents, giving them greater opportunities to enter work or training.
"These figures show that Scotland has the economic potential to be an independent country. With the full powers of independence we could do more to get people into work and give employers access to the skills they need to grow their business, strengthening our economy and creating jobs."