Study to Evaluate the Safety and Efficacy of CAT-354

Inclusion Criteria: * Male or female subjects * Age 18 to 65 years at the time of Screening * Subjects must have a body mass index (BMI) between 18 and 40 kilogram per square meter (kg/m\^2) * Written informed consent obtained from the subject prior to performing any protocol related procedures, including Screening evaluations * Physician-diagnosed moderate-to-severe, persistent asthma requiring treatment with appropriate asthma controller medication * Shows forced expiratory volume in 1 second (FEV1) reversibility postbronchodilator of greater than or equal to (\>=)12 percent and \>=200 milliliter (mL) or have shown such values in a previous test within the last year, or have a positive airway hyperresponsiveness (AHR) test result in the last year * Pre-bronchodilator FEV 1 value \>=40 percent of individual predicted value at Visits 1 and 3 * Uncontrolled asthma consistent with Expert Panel Report (EPR)-3. In the 2 to 4 weeks preceding Screening, subjects should have a history of 1 or more of the following: Daytime asthma symptoms \>=2 days/week, Nighttime awakening \>=1 night/week, Salbutamol use \>=2 days/week * An Asthma control questionnaire (ACQ) score \>=1.5 at Visits 1 and 3 * At least 1 occurrence of asthma exacerbation in the past year that required an unscheduled medical encounter * Men, unless surgically sterile, must likewise practice 2 effective methods of birth control (condom with spermicide) and must use such precautions from Day 1 through Study Day 169 * Ot…