A nationwide survey carried out by the Tamedia group found that for 70 percent of respondents healthcare costs were the biggest concern and outweighed worries about the country's old-age pension scheme (57 percent).
Other important areas of concern were migration (49 percent), relations with Europe (47 percent) and asylum (45 percent).
The environment was a top concern to 37 percent of the almost 15,000 respondents while just 22 percent gave terrorism as their main worry.
Health insurance premiums have risen by 158 percent in just over 20 years, according to online portal 20 minutes.
In 2018 they went up again, by four percent.
Basic health insurance is compulsory for everyone in Switzerland. There are over 60 private insurers all offering the same level of cover.
The survey found that 71 percent of Swiss supported an initiative by the Christian Democrats for a brake on premium costs.
The centre-right party is demanding that the federal government and the cantons take measures to reduce healthcare costs when these reach a certain level.
A rival initiative by the Social Democrats, backed by around 62 percent of respondents, aims to ensure that healthcare premiums never exceed 10 percent of a household's disposable income.
The survey found that 15 months ahead of federal elections the conservative Swiss People's Party remains the most popular political party, with the backing of 29 percent of Swiss, followed by the Social Democrats which are on 19 percent.