The Kingdom spent $67bn last year, a 14 percent increase on 2012, meaning it leapfrogged the UK, Japan and France in budget terms.
Saudi military spending has more than doubled in 10 years, according to the institute's report, which was released on Monday. It is still, however, dwarfed by the three nations above it, with Russia spending $87.8bn, China $188bn and the US spending $640bn.
Spending in the Middle East overall increased by 4 percent in 2013 to an estimated $150bn. Bahrain's increased by 26 percent, while Iraq's expenditure increased 27 percent, according to SIPRI.
Military spending data for Iran, Qatar, Syria and the UAE was not available for 2013, however.
Sam Perlo-Freeman, the director of SIPRI’s military expenditure program, said the missing data meant the estimated Middle East total was "highly uncertain".
"This reflects the general opacity of military spending in the region, and even where data is available it may not cover all military spending," he said.
Total world military spending was $1.75 trillion - down 1.9 percent on the previous year and mainly due to a 7.8 percent cut in US expenditure, and austerity measures in Europe. Nevertheless, the US still accounted for 37 percent of all military spending.
The trend was still upwards in many other nations, said Perlo-Freeman, "While in some cases it is the natural result of economic growth or a response to genuine security needs, in other cases it represents a squandering of natural resource revenues, the dominance of autocratic regimes, or emerging regional arms races."
Military spending in Africa increased by 8.3 percent in 2013, reaching an estimated $44.9bn. More than two-thirds of the African nations for which data is available increased military spending in 2013, said SIPRI.
Algeria became the first country in Africa with military spending over $10bn, an increase of 8.8 percent since 2012, and of 176 percent since 2004.
Meanwhile, Angola increased its spending by 36 percent in 2013. High oil revenues appear to be a factor driving both Algeria’s and Angola’s spending increases, SIPRI said.
NTJ/SHI