There is a short visit visa availiable to the following countries which is valid for two weeks. You will have to pay 20 Omani Rials at the airport.
Andorra, Austria, Belgium, Bosnia & Herzegovina, Britain, Bulgaria, Croatia, Cyprus, Czech Rep., Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Liechtenstein, Lithuania, Luxembourg, Macedon, Malta, Moldova, Monaco, Netherlands, Norway, Poland, Portugal, Rumania, San Marino, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey, Vatican, Argentina, Bolivia, Brazil, Chile, Colombia, Ecuador, French Guiana, Paraguay, Peru, Suriname, Uruguay, Venezuela, Australia, Brunei Dar al-Salam, Canada, Hong Kong, Indonesia, Japan, Lebanon, Malaysia, New Zealand, Seychelles, Singapore, South Africa, South Korea, Taiwan, Thailand, Tunis and United States.
Other nationalities will need to apply for a visa ahead of time at their nearest embassy or consulate.
Oman Visa information
Oman embassies
Foreign embassies in Oman