Grundberg last visited the capital Sanaa, controlled by the Iran-backed Huthis, in May 2023 for meetings with the rebels' leaders in an earlier effort to advance a roadmap for peace.
The envoy's current visit "is part of his ongoing efforts to urge for concrete and essential actions... for advancing the peace process", Grundberg's office said in a statement.
Yemen has been at war since 2014, when the Huthis forced the internationally recognised government out of Sanaa. The rebels have also seized population centres in the north.
In March 2015, a Saudi-led coalition intervened to prop up the beleaguered government.
A UN-brokered ceasefire in April 2022 calmed fighting and in December 2023 the warring parties committed to a peace process.
But tensions have surged during the Israel-Hamas war in Gaza, as the Huthis struck Israeli targets and international shipping in the Red Sea and Gulf of Aden, in a campaign the rebels say is in solidarity with Palestinians.
In response to the Huthi attacks, Israel as well as the United States and Britain have hit Huthi targets in Yemen over the past year. One Israeli raid hit Sanaa's international airport.
Grundberg's office said his visit would also "support the release of the arbitrarily detained UN, NGO, civil society and diplomatic mission personnel".
Dozens of staff from UN and other humanitarian organisations have been detained by the rebels, most of them since June, with the Huthis accusing them of belonging to a "US-Israeli spy network", a charge the United Nations denies.
