"The sharp rise in forced displacement reflects weaknesses in international cooperation, and declining capacity to prevent, contain and resolve conflicts," Grandi told the council.
He pointedly asked: "Have we become unable to broker peace?".
The remarks came as Western powers were again locked in a row with Russia over a plan to hold a peace conference to end Syria's six-year war that they say could sideline UN-led talks.
The Security Council also appears deadlocked on how to respond to the refugee crisis in Myanmar after a military campaign forced more than 600,000 Muslim Rohingya to flee to Bangladesh.
Grandi, who became the UN high commissioner for refugees last year, also listed worsening crises in Libya, Mali, Ukraine, Yemen and Africa's Lake Chad Basin.
Fresh violence in Burundi, South Sudan and the Central African Republic have triggered new outflows of refugees, he said.
Grandi said proxy wars were being waged, leaving diplomacy at the wayside, and complained that "the focus is on short-term interests rather than long-term collective stability."
The Security Council has a mandate under the charter to safeguard international peace and security, but its efforts in Syria, Yemen, South Sudan, Libya and other trouble spots have fallen short.
As refugee chief, Grandi said he bore witness to "the direct impact of these failures, every day, on the lives of tens of millions of people" who are hoping for a political solution the conflicts they have fled.
"The uprooted people are counting on your leadership to help deliver those solutions," he told the council.