An atomizer includes a liquid storage assembly, an adjustment assembly detachably mounted at one end of the liquid storage assembly, and an atomizing assembly mounted in the liquid storage assembly. An air intake passage is defined in the adjustment assembly. The atomizing assembly includes an atomizing head and an atomizing sleeve sleeved on the atomizing head. The atomizing head includes an atomizing core. At least one air intake groove is axially defined in the outer surface of the sidewall of the atomizing core and communicates with the air intake passage. An air intake hole is defined at a lower end of each air intake groove and communicates with a corresponding air intake groove. The external air enters into the air intake groove through the air intake passage and then enters into the inside of the atomizing core through the air intake hole. An electronic cigarette with the atomizer is also provided.