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Local media reports had said PCB chairman Ijaz Butt was ready to strip Afridi of the captaincy, and was angry at comments made by the all-rounder about three Pakistani cricketers at the centre of a spot-fixing scandal.
But the 30-year-old Afridi kept the role despite losing the Twenty20 series against New Zealand last month.
Misbah-ul-Haq, who led Pakistan in the two-Test series against New Zealand, will be Afridi's deputy.
Veteran batsman Mohammad Yousuf was left out, raising fears the 36-year-old will not make the final World Cup squad.
Wicketkeeper Kamran Akmal, who was cleared by the PCB for selection after he too fell under the spotlight of the investigation into spot-fixing, was restored to the side for the New Zealand series.
Akmal has not been selected since the tour of England which ended in September last year, and his reputation was marred by spot-fixing allegations which led to the suspensions of Salman Butt, Mohammad Asif and Mohammad Aamer.
Former captain Shoaib Malik and Fawad Alam were overlooked.
The six-match one-day series, which starts in Wellington on January 22, will be Pakistan's last before the World Cup which is to be jointly hosted by India, Sri Lanka and Bangladesh from February 19 to April 2.
Squad: Shahid Afridi (captain), Misbah-ul-Haq (vice captain), Mohammad Hafeez, Kamran Akmal, Younis Khan, Asad Shafiq, Umar Akmal, Abdul Razzaq, Abdur Rehman, Saeed Ajmal, Shoaib Akhtar, Umar Gul, Wahab Riaz, Sohail Tanveer, Tanveer Ahmed, Ahmed Shahzad