This Jewish group graded countries from A to F according to their efforts and results in related investigations and court trials.
Croatia received the highest grade.
"The United States, Croatia, Australia and several EU countries rated highest, while Austria, Sweden, Norway, Romania, Estonia, Lithuania, Ukraine and Syria were ranked at the bottom," Reuters reported.
The centre singled out Austria for "consistent failure" to prosecute Milivoj Asner, "a police chief under Croatia's Nazi-allied Ustashe regime during World War Two whom the centre said has been living in the Austrian city of Klagenfurt," the news agency reported.
According to Reuters, Austrian justice officials could not be reached for comment.
"Responding to Simon Wiesenthal Center complaints last year, justice officials said Asner, in his early 90s, had both Austrian and Croatian citizenship and they did have a legal basis for 'surveillance measures'."
The centre criticised some other countries "for what it called a refusal in principle to investigate, let alone prosecute, suspected war criminals despite evidence they lived within their borders".
According to the group's report, 2005 saw a 320-percent rise in convictions, with dozens of new investigations against Holocaust perpetrators joining hundreds of other cases.