VATICAN CITY—Every year, Catholics around the world donate tens of millions of dollars to the pope. Bishops exhort the faithful to support the weak and suffering through the pope’s main charitable appeal, called Peter’s Pence.

What the church doesn’t advertise is that most of that collection, worth more than €50 million ($55 million) annually, goes toward plugging the hole in the Vatican’s own administrative budget, while as little as 10% is spent on charitable works, according to people familiar with the funds.

The little-publicized breakdown of how the Holy See spends Peter’s Pence, known only among senior Vatican officials, is raising concern among some Catholic Church leaders that the faithful are being misled about the use of their donations, which could further hurt the credibility of the Vatican’s financial management under Pope Francis.

The Vatican is currently embroiled in a scandal over opaque real-estate investments in London, which has triggered a power struggle within the Vatican’s bureaucracy and led to the dismissal of its chief financial regulator. Last month, the Vatican was suspended from an international network of anti-money-laundering watchdogs.

Meanwhile, the Holy See is struggling with a growing budget deficit, with the pope warning cardinals of the “grave impact” on the body’s economic future. The Vatican’s continuing financial problems reflect a lack of progress on improving its management and finances, which Pope Francis was elected in 2013 with a mandate to overhaul, following allegations of corruption, waste and incompetence there.