Inspections are taking place at city shopping centres, bars and nightclubs, as part the nationwide Project Griffin operation.
Glasgow's most senior officer today vowed his officers are "alive" to any potential terrorist activities.
Chief Superintendent Andy Bates said: "It's in our DNA to prevent what happened at Glasgow Airport happening again.
"Terrorism can happen anywhere. Anywhere with crowds can be a target.
"But we are absolutely alive to anything happening."
The measures are part of a project to thwart the kind of attack which struck Glasgow Airport in 2007.
Counter-terrorism officials routinely visit venues and buildings where large groups of people congregate.
Previous terror attacks on congested areas include the 2007 Glasgow Airport attack, the 2005 bombings in London, and the Boston Marathon bombing in 2013.
However, senior officers stress there is no specific threat to Glasgow.
Mr Bates, Divisional Commander for Greater Glasgow, said: "Terrorism is an ongoing issue, but our cops on the ground know what to look for.
"If they see anyone acting suspciously, they will challenge them.
"And because we are part of one force, we can call on national support units at any time.
"The national force allows me to be able to pick up the phone and have access to any specialist units we may need."
Project Griffin's primary mission is to deter, detect and counter terrorist activity and crime.
Police in London introduced the system in 2004, following the 2001 terror attacks on the World Trade Centre in New York.
Since then, Project Griffin has been extended across the UK, USA, Canada and Australia.
The Evening Times previously told how city centre workers took part in a counter-terrorism awareness training scheme.
Firearms officers, detectives and specialist security advisers took part in the training session, which was part of the continuing initiative,
Staff, including security guards, were trained to deal with a host of different emergencies, including an "active shooter" and bomb alert.
Workers also received training on procedures to deal with possible bombs and how to spot suspicious behaviour, and how to treat suspicious packages.
Those behind the project claim the training helps police fight any threat by "engaging, encouraging and enabling members of the community" to work with officers.
Council bosses have also welcomed the initiative.
A Glasgow City Council spokesman said: "Project Griffin will play an important role in keeping the people and businesses of Glasgow informed on counter-terrorism an crime prevention issues.
"Any initiative that helps to protect our communities from terrorism, extremism and crime is to be welcomed."