NSPCC Scotland said that there was a 44.5% increase in referrals made to social work services or police.
A total of 176 referrals - the highest number in the country - were made to agencies in Glasgow during 2012/13.
Of 1920 calls to the Childline helpline from people in Scotland during this time, around 60% were sufficiently serious to merit a referral to police or social services.
The charity said 1166 referrals were made in 2012/13, involving 1807 children in Scotland.
Half of Scottish callers had waited more than a month to report their concerns and a further quarter had delayed speaking out for more than six months.
The charity urged people to act quickly if they are concerned about a child.
Matt Forde, national head of service for NSPCC Scotland, said: "These figures demon-strate clearly the important role of the NSPCC helpline in identifying families and children in need of support in Scotland.
"Without the will-ingness of friends, families and comm-unities to take action, children affected by abuse and neglect might never enjoy the childhood they deserve.
"Last year, the majority of those whose contacts resulted in a referral were members of the public (59%).
"We would urge any-one with concerns to reach out immediately.
"It's important to understand that if you are mistaken, a family will not be separated."
The leading cause for referrals in Scotland last year was neglect (46%), with physical abuse and sexual abuse also reported as significant concerns.
Anyone worried can contact the NSPCC on 0808 800 5000, text 88858 or email email@example.com 24/7.
Calls can be made anonymously.