A light cap without vizor and often ornamental, usually worn by smokers.(noun)
The Century Dictionary (Public Domain)
Use "smoking-cap" in a sentence
"STOCKMANN in dressing-gown, slippers and a smoking-cap, is bending down and raking with an umbrella under one of the cabinets."
"Here Louis made himself comfortable in his chair and smoking-cap, enjoying the fragrance of a cigar for something like half-an-hour."
"He chatted a little with him, reproached him for having quite forgotten his aunt and himself, listened to fresh praises of that heart of gold, the princess, who had just sent Kupfer from Yaroslav a smoking-cap embroidered with fish-scales ... and all at once, sitting just opposite Kupfer and looking him straight in the face, he announced that he had been a journey to Kazan."