The SonntagsBlick newspaper reported new statistics showing the number of applications increased by 17 percent last year over the previous year.
The statistics from all 26 cantons showed that there were 29,146 applications for gun ownership made in 2015.
All cantons with the exception of Jura in the northwest reported an increase. In most cases there was a double-digit jump in requests.
Demand was highest in Obwalden (plus 49 percent), Lucerne (plus 34 percent) and Zug (33 percent).
And the trend looks set to continue this year. Figures provided by the cantons of St Gallen and Basel Country showed gun sales there were up 30 percent already this year, the paper said.
The increase in gun ownership is not down to people who shoot for a hobby, according to SonntagsBlick, as the number of those belonging to gun clubs has remained constant or even fallen in recent years.
There also appears to be no connection with army weapons. It has been the case for six years that anyone wanting to hold onto an army-issue gun following the end of their military service has needed a licence.
Police sources told the paper the likely reason for the boom in applications was the rise in fears over terrorism.
The 2016 security report by the Centre for Security Studies of the Federal Institute of Technology (ETH) Zurich backed this up, according to the paper.
The report found growing pessimism about the global political situation with 87 percent of the view that more needed to be done to fight terrorism.
To own a gun in Switzerland you must file an application with the police, be over 18 and be able to prove you do not pose a danger to yourself or others.
Gun owners additionally need a licence to carry their weapon, and that requires passing a test.