If you are a resident in Dubai you should be able to sponsor your family members (wife, husband, children) allowing them to stay in the country as long as you are here.
If the family member is already in Dubai on a visit visa you can apply as below and have the visa swapped.

Prerequisites
Sponsor: 

• Minimum monthly salary of Dhs.4,000, or Dhs.3,000 with accommodation allowance.
• UAE residence visa (employment).

Family member:

• Medical completed (and passed). See Taking the medical test.
• Resident Identity Card application is underway.
• Minimum six months’ validity on passport of family member.
• Sons must be under the age of 18 or in full-time education (visa must be renewed annually in case of the latter).
• Daughters older than 18 can remain on their father’s sponsorship as long as they are unmarried.

What to bring
​Sponsor:

• Passport and Resident ID (copies).
• Tenancy contract attested through Ejari, the online system of the Real Estate Regulatory Authority (RERA). If the agreement is in your employer’s name, you should add your name in brackets.
• Employment contract to be attested by GDRFA. If the sponsor works with a government or semi-government department, then the salary certificate does not need attestation.
• Last three months’ bank statements. Online printed statement will not be accepted.
• Copy and original receipt of financial security (Dhs.5,000) if sponsoring parents or first or second degree relatives for humanitarian situation.
• Dhs.310 (plus typing fee) per family member.

Family member:

• Passport (original and copies).
• Visit visa if already in Dubai.
• Medical test certificate if over 15 years old (original).
• Two passport-sized photos (with a white background).
• Marriage certificate (attested by UAE embassy in home country and Ministry of Foreign Affairs in UAE).
• Birth certificate of child (attested by UAE embassy in home country and Ministry of Foreign Affairs in UAE).
• Resident ID application form certified by the Registration Centre at the Emirates Identity Authority (EIDA).
• Certificate from educational institute if male child over the age of 18.

Procedure

• General Directorate of Residency and Foreigners Affairs (GDRFA).
• First visit a typing centre with documents to complete relevant application form.
• Submit your application at the Family Entry Permit counter at the GDRFA along with supporting documents. 
• Family member’s passport with residence visa stamp can be collected within three to five days, or you can pay Dhs.15 to have it couriered to you.