In case you stay up to 14 days and you are national of one of the following countries you will receive a visa on arrival and don’t need to apply for one in advance. 

Albania

Algeria

Andorra

Argentina

Armenia

Australia

Austria

Azerbaijan

Belarus

Belgium

Bhutan

Bolivia

Bosnia and Herzegovina

Brazil

Brunei Darussalam

Bulgaria

Canada

Chile

China (includes Hong Kong and Macau)

Colombia

Costa Rica

Croatia

Cuba

Cyprus

Czech Republic

Denmark

Ecuador

Estonia

Eygpt

Finland

France

French Guinea

Georgia

Germany

Greece

Guatemala

Honduras

Hungary

Iceland

India

Indonesia

Iran

Ireland

Italy

Japan

Jordan

Kazakhstan

Kyrgyzstan

Laos

Latvia

Lebanon

Liechtenstein

Lithuania

Luxembourg

Macedonia

Malaysia

Maldives

Malta

Mauritania

Mexico

Moldova

Monaco

Morocco

Netherlands

New Zealand

Nicaragua

Norway

Panama

Paraguay

Peru

Poland

Portugal

Romania

Russia

Salvador

San Marino

Serbia

Seychelles

Singapore

Slovakia

Slovenia

South Africa

South Korea

Spain

Suriname

Sweden

Switzerland

Taiwan

Tajikistan

Thailand

Tunisia

Turkey

Turkmenistan

United Kingdom

Ukraine

Uruguay

United States

Uzbekistan

Vatican

Venezuela

Vietnam

In case you are staying longer than 14 days and/or belong to other nationality you can easily apply on the Website of the Royal Oman Police for your eVisa 

https://evisa.rop.gov.om/visa-eligibility?p_p_id=visawizard_WAR_visaeligibilitywizardportlet&p_p_lifecycle=0&p_p_state=normal&p_p_mode=view&p_p_col_id=column-1&p_p_col_count=1&_visawizard_WAR_visaeligibilitywizardportlet_myaction=recheck

Source: Foreign Ministry of Oman