Health boards received 3,000 complaints in 2012, slightly less in 2013, then 3,471 in 2014, and 955 so far in 2015.
Welsh Lib Dem leader Kirsty Williams said the "staggering" figures showed staff were "in desperate need of help".
The Welsh government said NHS staff numbers had risen by a third since devolution in 1999.
The Welsh Lib Dems asked health boards how many complaints they received from workers about a lack of qualified staff.
"These figures paint a picture of a Labour-run NHS that is under enormous strain and in desperate need of help," Ms Williams said.
"The Welsh Lib Dems' More Nurses Bill would see Wales become the first country in the UK with a legal duty on safe nurse staffing levels.
"It will save lives by ensuring a safe level of nurse staffing in our hospitals."
Eluned Parrott, Lib Dem AM for South Wales Central, denied the party was raising the issue now in an attempt to seek political leverage for its More Nurses Bill, which has reached the amendments stage in the assembly.
"Absolutely not," she told BBC Radio Wales' Good Morning Wales programme. "What we're raising here is a serious issue about the concerns that staff have within the NHS."
She said the bill was one way of looking to tackle the problem, but other staffing levels also needed looking at.
A Welsh government spokesman said: "Our commitment to the NHS is clear - more than 43% of the total Welsh budget is invested in our health service every year.
"There are more doctors, more nurses, more midwives, more paramedics and more dental staff working in the Welsh NHS today than there were 10 years ago."
NHS workers in Wales have made more than 10,000 complaints about staff shortages since 2012, according to research by the Liberal Democrats.